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\begin{algorithmic}[1]
\State Input: Two multi-sets of $n$ points $R,B$ in $Q_d$.
\State Output: A matching from $R$ to $B$.
\State$\triangleright$ The set B is shared across all threads
\Procedure{WeightedMatch}{$R,B$}
\For {$r \in R$}\Comment{All for loop statements run in parallel}
\State $b\gets\mathrm{BreadthFirstSearch}(r,B)$
\State $M\gets M\cup \{r\to b\}$
\EndFor
\State \textbf{return} $M$\Comment{M is the matching}
\EndProcedure
\Procedure{BreadthFirstSearch}{$r,B$}
\For{$i=1,...,d$}
\For{$v\in Q_d$, $\|v-r\|_1=i$}
\If{$v\in B$}
\State $B\gets B\setminus{v}$
\State \textbf{return} $v$\Comment{r matches to v}
\EndIf
\EndFor
\EndFor
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Input: Two multi-sets of $n$ points $R,B$ in $Q_d$.
\State Output: A matching from $R$ to $B$.
\State$\triangleright$ The set B is shared across all threads
\Procedure{WeightedMatch}{$R,B$}
\For {$r \in R$}\Comment{All for loop statements run in parallel}
\State $b\gets\mathrm{BreadthFirstSearch}(r,B)$
\State $M\gets M\cup \{r\to b\}$
\EndFor
\State \textbf{return} $M$\Comment{M is the matching}
\EndProcedure
\Procedure{BreadthFirstSearch}{$r,B$}
\For{$i=1,...,d$}
\For{$v\in Q_d$, $\|v-r\|_1=i$}
\If{$v\in B$}
\State $B\gets B\setminus{v}$
\State \textbf{return} $v$\Comment{r matches to v}
\EndIf
\EndFor
\EndFor
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2401.11562" | "2401.11562.tar.gz" | "2024-01-21" | {
"title": "enhancing selectivity using wasserstein distance based reweighing",
"id": "2401.11562",
"abstract": "given two labeled data-sets $\\mathcal{s}$ and $\\mathcal{t}$, we design a simple and efficient greedy algorithm to reweigh the loss function such that the limiting distribution of the neural network weights that result from training on $\\mathcal{s}$ approaches the limiting distribution that would have resulted by training on $\\mathcal{t}$. on the theoretical side, we prove that when the metric entropy of the input data-sets is bounded, our greedy algorithm outputs a close to optimal reweighing, i.e., the two invariant distributions of network weights will be provably close in total variation distance. moreover, the algorithm is simple and scalable, and we prove bounds on the efficiency of the algorithm as well. our algorithm can deliberately introduce distribution shift to perform (soft) multi-criteria optimization. as a motivating application, we train a neural net to recognize small molecule binders to mnk2 (a map kinase, responsible for cell signaling) which are non-binders to mnk1 (a highly similar protein). we tune the algorithm's parameter so that overall change in holdout loss is negligible, but the selectivity, i.e., the fraction of top 100 mnk2 binders that are mnk1 non-binders, increases from 54\\% to 95\\%, as a result of our reweighing. of the 43 distinct small molecules predicted to be most selective from the enamine catalog, 2 small molecules were experimentally verified to be selective, i.e., they reduced the enzyme activity of mnk2 below 50\\% but not mnk1, at 10$\\mu$m -- a 5\\% success rate.",
"categories": "stat.ml cs.lg q-bio.qm",
"doi": "",
"created": "2024-01-21",
"updated": "",
"authors": [
"pratik worah"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.11562"
} | "2024-03-15T07:03:20.799704" | {
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} | [] | "algorithm" | "6198b44e-7ef3-4092-abff-15603e4a2143" | 681 | easy |
|
\begin{algorithmic}[1]
\Require current node $u$, candidate node $v$, Walker $W$, {\sf HuGE} parameter $\mu$
\Ensure walker state updates
{\flushleft{{\bf sendStateQuery($u$, $v$, $W$)}}} %//{submit the walker-to-vertex query messages and process the state queries}
\State{$P(u,v) = Z\left(\frac{1}{deg(u)-Cm(u, v)}\cdot \max \left\{\frac{deg(u)}{deg(v)}, \frac{deg(v)}{deg(u)} \right\} \right)$} // Eq.~\ref{accept_CNHRW}
{\flushleft{{\bf getStateQueryResult($W, P(u,v)$)}}} %// {return results to querying walkers for retrieving the state and decide sampling outcome}
\State{generate a random number $\eta \in\left[0,1\right]$}
\If{$P(u,v)> \eta $}
\State{$W.path$.append($v$), $W.cur$ = $v$, $W.steps$ ++}
\State{$L$ = $W.steps$}
\State compute $H(W)$ and $R\left(H(W),L\right)$ // Eq.~\ref{path_entropy}, \ref{path_corr}
\If{$R^2(H(W),L) < \mu$}
\State terminate the walk
\Else
\State{generate another candidate node $t$ of $v$}
\State{sendStateQuery($v$, $t$, $W$)}
\EndIf
\Else
\State{backtrack to $u$ and generate another candidate node $v'$ of $u$}
\State{sendStateQuery($u$, $v'$, $W$)}
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require current node $u$, candidate node $v$, Walker $W$, {\sf HuGE} parameter $\mu$
\Ensure walker state updates
{\flushleft{{\bf sendStateQuery($u$, $v$, $W$)}}} %//{submit the walker-to-vertex query messages and process the state queries}
\State{$P(u,v) = Z\left(\frac{1}{deg(u)-Cm(u, v)}\cdot \max \left\{\frac{deg(u)}{deg(v)}, \frac{deg(v)}{deg(u)} \right\} \right)$} // Eq.~\ref{accept_CNHRW}
{\flushleft{{\bf getStateQueryResult($W, P(u,v)$)}}} %// {return results to querying walkers for retrieving the state and decide sampling outcome}
\State{generate a random number $\eta \in\left[0,1\right]$}
\If{$P(u,v)> \eta $}
\State{$W.path$.append($v$), $W.cur$ = $v$, $W.steps$ ++}
\State{$L$ = $W.steps$}
\State compute $H(W)$ and $R\left(H(W),L\right)$ // Eq.~\ref{path_entropy}, \ref{path_corr}
\If{$R^2(H(W),L) < \mu$}
\State terminate the walk
\Else
\State{generate another candidate node $t$ of $v$}
\State{sendStateQuery($v$, $t$, $W$)}
\EndIf
\Else
\State{backtrack to $u$ and generate another candidate node $v'$ of $u$}
\State{sendStateQuery($u$, $v'$, $W$)}
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2303.15702" | "2303.15702.tar.gz" | "2024-02-25" | {
"title": "distributed graph embedding with information-oriented random walks",
"id": "2303.15702",
"abstract": "graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. the increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on twitter with over one billion edges. most existing graph embedding methods fall short of reaching high data scalability. in this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, distger, which can scale to embed billion-edge graphs. distger incrementally computes information-centric random walks. it further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. distger also improves the distributed skip-gram learning model to generate node embeddings by optimizing the access locality, cpu throughput, and synchronization efficiency. experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including knightking, distdgl, and pytorch-biggraph, distger exhibits 2.33x-129x acceleration, 45% reduction in cross-machines communication, and > 10% effectiveness improvement in downstream tasks.",
"categories": "cs.dc cs.lg",
"doi": "",
"created": "2023-03-27",
"updated": "2024-02-25",
"authors": [
"peng fang",
"arijit khan",
"siqiang luo",
"fang wang",
"dan feng",
"zhenli li",
"wei yin",
"yuchao cao"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.15702"
} | "2024-03-15T03:43:03.810720" | {
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} | [] | "algorithm" | "495ba26c-9d13-4916-8708-fb41c8065401" | 1121 | medium |
|
\begin{algorithmic}[1]
\Procedure{ModifiedGD}{$\nabla F, \hat{L}_{i, 0}, \delta_{(i, \cdot)}, R, \theta_{i, 0}, \kappa_{(i,\cdot)}, T^*, \ell, \gamma$}
\State $ \Delta \leftarrow 0 $ \Comment{Measure of predicted decrease of objective}
\For{$j = 0, 1, ..., T^*-1$}
\State $\alpha_{i,j} \leftarrow \delta_{(i,\cdot)} (2||\nabla F(\theta_{i,j})||^3 + ||\nabla F(\theta_{i,j})||^2\hat{L}_{i,j} )^{-1}$ \Comment{Step size computation}
\State $\theta_{i, j+1} \leftarrow \theta_{i,j} - \alpha_{i,j} \nabla F(\theta_{i,j})$ \Comment{Gradient step}
\State $\Delta \leftarrow \Delta - \delta_{(i,\cdot)}^2\left( 4||\nabla F(\theta_{i,j})||^3 + 2\hat{L}_{i,j}||\nabla F(\theta_{i,j}) ||^2 \right)^{-1}$ \Comment{Update predicted decrease}
\If{ $|| \theta_{i,j} - \theta_{i,j+1} || \ge 10^{-10}$ }
\State $\hat{L}_{i,j+1} \leftarrow \Call{UpdateL}{\nabla F, \theta_{i,j}, \theta_{i,j+1}, \hat{L}_{i,j}, \kappa_{(i,\cdot)}, \ell}$ \Comment{Update local Lipschitz estimate}
\Else
\State $\hat{L}_{i,j+1} \leftarrow \hat{L}_{i,j}$
\EndIf
\State $ \delta_{cond} \leftarrow ||\nabla F(\theta_{i,j+1})||^2 \not\in (\delta_{(i,\cdot)}, \gamma\delta_{(i,\cdot)})$
\If{$\delta_{cond}$ or $||\theta_{i,j+1}-\theta_{i,0}|| > R$ or stop condition} \Comment{Check triggering events}
\State \Return{$\theta_{i,j+1},\hat{L}_{i,j+1},\delta_{cond},\Delta$}
\EndIf
\EndFor
\State
\Return{$\theta_{i,T^*},\hat{L}_{i,T^*},\delta_{cond},\Delta$}
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\Procedure{ModifiedGD}{$\nabla F, \hat{L}_{i, 0}, \delta_{(i, \cdot)}, R, \theta_{i, 0}, \kappa_{(i,\cdot)}, T^*, \ell, \gamma$}
\State $ \Delta \leftarrow 0 $ \Comment{Measure of predicted decrease of objective}
\For{$j = 0, 1, ..., T^*-1$}
\State $\alpha_{i,j} \leftarrow \delta_{(i,\cdot)} (2||\nabla F(\theta_{i,j})||^3 + ||\nabla F(\theta_{i,j})||^2\hat{L}_{i,j} )^{-1}$ \Comment{Step size computation}
\State $\theta_{i, j+1} \leftarrow \theta_{i,j} - \alpha_{i,j} \nabla F(\theta_{i,j})$ \Comment{Gradient step}
\State $\Delta \leftarrow \Delta - \delta_{(i,\cdot)}^2\left( 4||\nabla F(\theta_{i,j})||^3 + 2\hat{L}_{i,j}||\nabla F(\theta_{i,j}) ||^2 \right)^{-1}$ \Comment{Update predicted decrease}
\If{ $|| \theta_{i,j} - \theta_{i,j+1} || \ge 10^{-10}$ }
\State $\hat{L}_{i,j+1} \leftarrow \Call{UpdateL}{\nabla F, \theta_{i,j}, \theta_{i,j+1}, \hat{L}_{i,j}, \kappa_{(i,\cdot)}, \ell}$ \Comment{Update local Lipschitz estimate}
\Else
\State $\hat{L}_{i,j+1} \leftarrow \hat{L}_{i,j}$
\EndIf
\State $ \delta_{cond} \leftarrow ||\nabla F(\theta_{i,j+1})||^2 \not\in (\delta_{(i,\cdot)}, \gamma\delta_{(i,\cdot)})$
\If{$\delta_{cond}$ or $||\theta_{i,j+1}-\theta_{i,0}|| > R$ or stop condition} \Comment{Check triggering events}
\State \Return{$\theta_{i,j+1},\hat{L}_{i,j+1},\delta_{cond},\Delta$}
\EndIf
\EndFor
\State
\Return{$\theta_{i,T^*},\hat{L}_{i,T^*},\delta_{cond},\Delta$}
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2309.10894" | "2309.10894.tar.gz" | "2024-02-15" | {
"title": "a novel gradient methodology with economical objective function evaluations for data science applications",
"id": "2309.10894",
"abstract": "gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges of optimization problems arising in data science. focusing on data science applications with expensive objective function evaluations yet inexpensive gradient function evaluations, gradient methods that never make objective function evaluations are either being rejuvenated or actively developed. however, as we show, such gradient methods are all susceptible to catastrophic divergence under realistic conditions for data science applications. in light of this, gradient methods which make use of objective function evaluations become more appealing, yet, as we show, can result in an exponential increase in objective evaluations between accepted iterates. as a result, existing gradient methods are poorly suited to the needs of optimization problems arising from data science. in this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent catastrophic divergence and avoid an explosion in objective evaluations between accepted iterates. our methodology allows for specific procedures that can make use of specific step size selection methodologies or search direction strategies, and we develop a novel step size selection methodology that is well-suited to data science applications. we show that a procedure resulting from our methodology is highly competitive with standard optimization methods on cutest test problems. we then show a procedure resulting from our methodology is highly favorable relative to standard optimization methods on optimization problems arising in our target data science applications. thus, we provide a novel gradient methodology that is better suited to optimization problems arising in data science.",
"categories": "math.oc stat.co",
"doi": "",
"created": "2023-09-19",
"updated": "2024-02-15",
"authors": [
"christian varner",
"vivak patel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2309.10894"
} | "2024-03-15T05:23:50.845023" | {
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} | [] | "algorithm" | "d5824813-2875-4568-bb05-f16712f12f47" | 1447 | hard |
|
\begin{algorithmic}[1]
\State \textbf{Input:} Stock data for two assets $S_1$ and $S_2$, buy threshold, sell threshold
\State \textbf{Output:} Trade signals for pairs trading
\State
\Procedure{Compute Hedge Ratio}{data1, data2}
\State model $\gets$ perform OLS regression (data1, data2)
\State \Return model.params$[1]$
\EndProcedure
\State
\Procedure{Initialize}{fast, slow}
\State hedge$\_$ratio $\gets$ \Call{Compute Hedge Ratio}{$S_1$, $S_2$}
\State Calculate spread $\gets$ $S_1$$-$hedge$\_$ratio $\times$ $S_2$
\State fast$\_$ema $\gets$ \Call{EMA}{spread, fast}
\State slow$\_$ema $\gets$ \Call{EMA}{spread, slow}
\State apo$\_$spread $\gets$ fast$\_$ema$-$slow$\_$ema
\State position $\gets 0$
\EndProcedure
\State
\Procedure{Next}{buy threshold, sell threshold}
\State \textbf{if}{~apo$\_$spread $<$ buy$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Buy for $S_1$ and Sell Short for $S_2$
\State \textbf{else if}{apo$\_$spread $>$ sell$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Sell Short for $S_1$ and Buy for $S_2$
\State \textbf{end if}
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input:} Stock data for two assets $S_1$ and $S_2$, buy threshold, sell threshold
\State \textbf{Output:} Trade signals for pairs trading
\State
\Procedure{Compute Hedge Ratio}{data1, data2}
\State model $\gets$ perform OLS regression (data1, data2)
\State \Return model.params$[1]$
\EndProcedure
\State
\Procedure{Initialize}{fast, slow}
\State hedge$\_$ratio $\gets$ \Call{Compute Hedge Ratio}{$S_1$, $S_2$}
\State Calculate spread $\gets$ $S_1$$-$hedge$\_$ratio $\times$ $S_2$
\State fast$\_$ema $\gets$ \Call{EMA}{spread, fast}
\State slow$\_$ema $\gets$ \Call{EMA}{spread, slow}
\State apo$\_$spread $\gets$ fast$\_$ema$-$slow$\_$ema
\State position $\gets 0$
\EndProcedure
\State
\Procedure{Next}{buy threshold, sell threshold}
\State \textbf{if}{~apo$\_$spread $<$ buy$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Buy for $S_1$ and Sell Short for $S_2$
\State \textbf{else if}{apo$\_$spread $>$ sell$\_$threshold} \textbf{then}
\State \hspace{1cm} Execute Sell Short for $S_1$ and Buy for $S_2$
\State \textbf{end if}
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2401.14761" | "2401.14761.tar.gz" | "2024-01-26" | {
"title": "esg driven pairs algorithm for sustainable trading: analysis from the indian market",
"id": "2401.14761",
"abstract": "this paper proposes an algorithmic trading framework integrating environmental, social, and governance (esg) ratings with a pairs trading strategy. it addresses the demand for socially responsible investment solutions by developing a unique algorithm blending esg data with methods for identifying co-integrated stocks. this allows selecting profitable pairs adhering to esg principles. further, it incorporates technical indicators for optimal trade execution within this sustainability framework. extensive back-testing provides evidence of the model's effectiveness, consistently generating positive returns exceeding conventional pairs trading strategies, while upholding esg principles. this paves the way for a transformative approach to algorithmic trading, offering insights for investors, policymakers, and academics.",
"categories": "q-fin.tr",
"doi": "",
"created": "2024-01-26",
"updated": "",
"authors": [
"eeshaan dutta",
"sarthak diwan",
"siddhartha p. chakrabarty"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.14761"
} | "2024-03-15T05:30:05.430403" | {
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} | [] | "algorithm" | "d4f074dd-00b8-4ebd-9eff-3126db854c98" | 1105 | medium |
|
\begin{algorithm}
GPB(N) Algorithm
\end{algorithm}
| \begin{algorithm}
GPB(N) Algorithm
\end{algorithm} | "https://arxiv.org/src/2402.08051" | "2402.08051.tar.gz" | "2024-02-12" | {
"title": "on bayesian filtering for markov regime switching models",
"id": "2402.08051",
"abstract": "this paper presents a framework for empirical analysis of dynamic macroeconomic models using bayesian filtering, with a specific focus on the state-space formulation of dynamic stochastic general equilibrium (dsge) models with multiple regimes. we outline the theoretical foundations of model estimation, provide the details of two families of powerful multiple-regime filters, imm and gpb, and construct corresponding multiple-regime smoothers. a simulation exercise, based on a prototypical new keynesian dsge model, is used to demonstrate the computational robustness of the proposed filters and smoothers and evaluate their accuracy and speed for a selection of filters from each family. we show that the canonical imm filter is faster and is no less, and often more, accurate than its competitors within imm and gpb families, the latter including the commonly used kim and nelson (1999) filter. using it with the matching smoother improves the precision in recovering unobserved variables by about 25 percent. furthermore, applying it to the u.s. 1947-2023 macroeconomic time series, we successfully identify significant past policy shifts including those related to the post-covid-19 period. our results demonstrate the practical applicability and potential of the proposed routines in macroeconomic analysis.",
"categories": "econ.em",
"doi": "",
"created": "2024-02-12",
"updated": "",
"authors": [
"nigar hashimzade",
"oleg kirsanov",
"tatiana kirsanova",
"junior maih"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.08051"
} | "2024-03-15T04:21:14.605813" | {
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} | [] | "algorithm" | "75bee723-8648-4b9d-82cd-341a3bad5259" | 50 | easy |
|
\begin{algorithmic}[1]
\State Initialize an empty list $l$
\For{\textbf{each} $i$ \textbf{in} $producers$}
\For{$t$ \textbf{in} $[500, 900)$}
\If{$\forall x \in \{p_{it},p_{i(t+1)},\dots,p_{i1000}\}(x < \epsilon)$}
\State $l$\textbf{.push}(True)
\State \textbf{break}
\EndIf
\EndFor
\State $l$\textbf{.push}(False)
\EndFor
\If{$\forall \text{y} \in l$\text{(y==True)}}
\State \textbf{return} $"Equilibrium"$
\Else
\State \textbf{return} $"Disequilibrium"$
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Initialize an empty list $l$
\For{\textbf{each} $i$ \textbf{in} $producers$}
\For{$t$ \textbf{in} $[500, 900)$}
\If{$\forall x \in \{p_{it},p_{i(t+1)},\dots,p_{i1000}\}(x < \epsilon)$}
\State $l$\textbf{.push}(True)
\State \textbf{break}
\EndIf
\EndFor
\State $l$\textbf{.push}(False)
\EndFor
\If{$\forall \text{y} \in l$\text{(y==True)}}
\State \textbf{return} $"Equilibrium"$
\Else
\State \textbf{return} $"Disequilibrium"$
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2401.07070" | "2401.07070.tar.gz" | "2024-01-13" | {
"title": "a dynamic agent based model of the real economy with monopolistic competition, perfect product differentiation, heterogeneous agents, increasing returns to scale and trade in disequilibrium",
"id": "2401.07070",
"abstract": "we have used agent-based modeling as our numerical method to artificially simulate a dynamic real economy where agents are rational maximizers of an objective function of cobb-douglas type. the economy is characterised by heterogeneous agents, acting out of local or imperfect information, monopolistic competition, perfect product differentiation, allowance for increasing returns to scale technology and trade in disequilibrium. an algorithm for economic activity in each period is devised and a general purpose open source agent-based model is developed which allows for counterfactual inquiries, testing out treatments, analysing causality of various economic processes, outcomes and studying emergent properties. 10,000 simulations, with 10 firms and 80 consumers are run with varying parameters and the results show that from only a few initial conditions the economy reaches equilibrium while in most of the other cases it remains in perpetual disequilibrium. it also shows that from a few initial conditions the economy reaches a disaster where all the consumer wealth falls to zero or only a single producer remains. furthermore, from some initial conditions, an ideal economy with high wage rate, high consumer utility and no unemployment is also reached. it was also observed that starting from an equal endowment of wealth in consumers and in producers, inequality emerged in the economy. in majority of the cases most of the firms(6-7) shut down because they were not profitable enough and only a few firms remained. our results highlight that all these varying outcomes are possible for a decentralized market economy with rational optimizing agents.",
"categories": "econ.th cs.ma",
"doi": "",
"created": "2024-01-13",
"updated": "",
"authors": [
"subhamon supantha",
"naresh kumar sharma"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.07070"
} | "2024-03-15T06:13:08.276479" | {
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} | [] | "algorithm" | "596d1a2a-5955-45c6-abc2-8a6ffce88a00" | 481 | easy |
|
\begin{algorithm}[!ht]
\caption{Discrete empirical interpolation method (DEIM)}\label{alg:DEIM}
\begin{algorithmic}[1]
\State \textbf{Input:} matrix $M \in \mathbb{R}^{n\times m}$ with orthonormal columns
\State \textbf{Output:} index set $I$ if cardinality $m$
\State $I = \{\mathsf{argmax}\ |M(:,1)|\}$
\For $k = 2,\dots,m$
\State $c = M(I,1:k-1)^{-1} M(I,k)$
\State $r = M(:,k) - M(:,1:k-1)c$
\State $I = I \cup \{\mathsf{argmax}\ |r|\}$
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[!ht]
\caption{Discrete empirical interpolation method (DEIM)}\begin{algorithmic}
[1]
\State \textbf{Input:} matrix $M \in \mathbb{R}^{n\times m}$ with orthonormal columns
\State \textbf{Output:} index set $I$ if cardinality $m$
\State $I = \{\mathsf{argmax}\ |M(:,1)|\}$
\For $k = 2,\dots,m$
\State $c = M(I,1:k-1)^{-1} M(I,k)$
\State $r = M(:,k) - M(:,1:k-1)c$
\State $I = I \cup \{\mathsf{argmax}\ |r|\}$
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2211.11338" | "2211.11338.tar.gz" | "2024-02-25" | {
"title": "approximation in the extended functional tensor train format",
"id": "2211.11338",
"abstract": "this work proposes the extended functional tensor train (eftt) format for compressing and working with multivariate functions on tensor product domains. our compression algorithm combines tensorized chebyshev interpolation with a low-rank approximation algorithm that is entirely based on function evaluations. compared to existing methods based on the functional tensor train format, the adaptivity of our approach often results in reducing the required storage, sometimes considerably, while achieving the same accuracy. in particular, we reduce the number of function evaluations required to achieve a prescribed accuracy by up to over 96% compared to the algorithm from [gorodetsky, karaman and marzouk, comput. methods appl. mech. eng., 347 (2019)].",
"categories": "math.na cs.na",
"doi": "",
"created": "2022-11-21",
"updated": "2024-02-25",
"authors": [
"christoph str\u00f6ssner",
"bonan sun",
"daniel kressner"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.11338"
} | "2024-03-15T03:21:44.181934" | {
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} | [] | "algorithm" | "080b212f-f820-4ed0-803b-0cd7ba5e82d4" | 467 | easy |
|
\begin{algorithm}
\caption{Multi-Period Transition Framework}\label{alg:MPTF}
\begin{algorithmic}[H]
\Require $P_0, \mathcal{T}, Y_{-L:0}, \mathbf{X}_{-L:0}, V_0, \mathbf{T}, C_0$, OPT, Forecaster, MarketObserver
\Ensure $Y_0^T\mathcal{T} + C_0 \leq V_0$
\State $t \gets 0$
\State $P_t \gets P_0$
\State $C_t \gets C_0$
\State $Y \gets Y_{-L:t}$
\While{$t \leq \mathbf{T}$}
\State $V_t \gets Y_t^TP_t + C_t$ \Comment{Calculate portfolio value at current timestep}
\State $\hat{Y}_{t+1:\mathbf{T}}\gets \text{Forecaster}(Y_{-L:t}, \mathbf{X}_{-L:t})$ \Comment{Predict unknown time steps with known information}
\State $Z_{t:\mathbf{T}}, W_{t:\mathbf{T}} \gets \text{OPT}([Y_t\ \hat{Y}_{t+1:\mathbf{T}}], P_t, C_t, \mathcal{T})$ \Comment{Run Optimization Policy}
\State $P_{t+1} \gets P_t + Z_t$ \Comment{Execute trades at current timestep}
\State $C_{t+1} \gets C_t - Y_t\cdot Z_t - F\Vec{1} \cdot W_t$ \Comment{Calculate cash}
\State $Y_{t+1} \gets \text{MarketObserver}()$ \Comment{Observe the market for new price information}
\State $t \gets t + 1$
\EndWhile
\Ensure $P_\mathbf{T} \geq \mathcal{T}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Multi-Period Transition Framework}\begin{algorithmic}
[H]
\Require $P_0, \mathcal{T}, Y_{-L:0}, \mathbf{X}_{-L:0}, V_0, \mathbf{T}, C_0$, OPT, Forecaster, MarketObserver
\Ensure $Y_0^T\mathcal{T} + C_0 \leq V_0$
\State $t \gets 0$
\State $P_t \gets P_0$
\State $C_t \gets C_0$
\State $Y \gets Y_{-L:t}$
\While{$t \leq \mathbf{T}$}
\State $V_t \gets Y_t^TP_t + C_t$ \Comment{Calculate portfolio value at current timestep}
\State $\hat{Y}_{t+1:\mathbf{T}}\gets \text{Forecaster}(Y_{-L:t}, \mathbf{X}_{-L:t})$ \Comment{Predict unknown time steps with known information}
\State $Z_{t:\mathbf{T}}, W_{t:\mathbf{T}} \gets \text{OPT}([Y_t\ \hat{Y}_{t+1:\mathbf{T}}], P_t, C_t, \mathcal{T})$ \Comment{Run Optimization Policy}
\State $P_{t+1} \gets P_t + Z_t$ \Comment{Execute trades at current timestep}
\State $C_{t+1} \gets C_t - Y_t\cdot Z_t - F\Vec{1} \cdot W_t$ \Comment{Calculate cash}
\State $Y_{t+1} \gets \text{MarketObserver}()$ \Comment{Observe the market for new price information}
\State $t \gets t + 1$
\EndWhile
\Ensure $P_\mathbf{T} \geq \mathcal{T}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.13126" | "2401.13126.tar.gz" | "2024-01-24" | {
"title": "optimizing transition strategies for small to medium sized portfolios",
"id": "2401.13126",
"abstract": "this work discusses the benefits of constrained portfolio turnover strategies for small to medium-sized portfolios. we propose a dynamic multi-period model that aims to minimize transaction costs and maximize terminal wealth levels whilst adhering to strict portfolio turnover constraints. our results demonstrate that using our framework in combination with a reasonable forecast, can lead to higher portfolio values and lower transaction costs on average when compared to a naive, single-period model. such results were maintained given different problem cases, such as, trading horizon, assets under management, wealth levels, etc. in addition, the proposed model lends itself to a reformulation that makes use of the column generation algorithm which can be strategically leveraged to reduce complexity and solving times.",
"categories": "q-fin.cp",
"doi": "",
"created": "2024-01-23",
"updated": "2024-01-24",
"authors": [
"nakul upadhya",
"alexandre granzer-guay"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.13126"
} | "2024-03-15T05:38:12.261498" | {
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} | [] | "algorithm" | "9d6c0f2d-70af-4e25-9cee-9bec2c661226" | 1119 | medium |
|
\begin{algorithm}
\caption{getNextStage(candidates, k)}\label{alg:te2rules_stagek}
\begin{algorithmic}
\State $newCandidates \gets []$
\\
\For{$r_1 \gets candidates$}
\For{$r_2 \gets candidates$}
\State $nodes_1 = r_1.sourceNodes$
\State $nodes_2 = r_2.sourceNodes$
\If{$|nodes_1 \cap nodes_2| = k - 2$}
\State $r \gets r_1 \& r_2$
\State $r.sourceNodes \gets n_1 \cup n_2$
\If{$|r.support| > \epsilon$}
\State $candidates.append(r)$
\EndIf
\EndIf
\EndFor
\EndFor
\\
\Return $newCandidates$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{getNextStage(candidates, k)}\begin{algorithmic}
\State $newCandidates \gets []$
\\
\For{$r_1 \gets candidates$}
\For{$r_2 \gets candidates$}
\State $nodes_1 = r_1.sourceNodes$
\State $nodes_2 = r_2.sourceNodes$
\If{$|nodes_1 \cap nodes_2| = k - 2$}
\State $r \gets r_1 \& r_2$
\State $r.sourceNodes \gets n_1 \cup n_2$
\If{$|r.support| > \epsilon$}
\State $candidates.append(r)$
\EndIf
\EndIf
\EndFor
\EndFor
\\
\Return $newCandidates$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2206.14359" | "2206.14359.tar.gz" | "2024-01-23" | {
"title": "te2rules: explaining tree ensembles using rules",
"id": "2206.14359",
"abstract": "tree ensemble (te) models, such as gradient boosted trees, often achieve optimal performance on tabular datasets, yet their lack of transparency poses challenges for comprehending their decision logic. this paper introduces te2rules (tree ensemble to rules), a novel approach for explaining binary classification tree ensemble models through a list of rules, particularly focusing on explaining the minority class. many state-of-the-art explainers struggle with minority class explanations, making te2rules valuable in such cases. the rules generated by te2rules closely approximate the original model, ensuring high fidelity, providing an accurate and interpretable means to understand decision-making. experimental results demonstrate that te2rules scales effectively to tree ensembles with hundreds of trees, achieving higher fidelity within runtimes comparable to baselines. te2rules allows for a trade-off between runtime and fidelity, enhancing its practical applicability. the implementation is available here: https://github.com/linkedin/te2rules.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2022-06-28",
"updated": "2024-01-23",
"authors": [
"g roshan lal",
"xiaotong chen",
"varun mithal"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.14359"
} | "2024-03-15T09:04:28.850184" | {
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} | [] | "algorithm" | "4838572e-3197-4b9d-96d2-c4263ddd219d" | 496 | easy |
|
\begin{algorithmic}[1]
\State Simulate $N$ random variables from $\text{Uniform}(0,1)$; Denote $\tilde{U}=(\tilde{U}_{(1)},...,\tilde{U}_{(N)})$ as the vector of $N$ simulated Uniformly distributed random variables
\State Denote $\tilde{Y}^{*}_{ij}=(\tilde{Y}^{*}_{ij,(1)},...,\tilde{Y}^{*}_{ij,(N)})$ as the vector of $N$ simulated variables for cell $(i,j)$ from the ensemble
\For{$n=1,..,N$}
\If{$\tilde{U}_{(n)} \in (\sum_{m=1}^{l-1}w_m,\sum_{m=1}^{l}w_m]$}
\State simulate a random variable from the $l^{th}$ component distribution, denoted as $\tilde{Y}_{ij}^{(l)}$
\State Set $\tilde{Y}^{*}_{ij,(n)}=\tilde{Y}_{ij}^{(l)}$
\EndIf
\EndFor
\State Repeat the above two steps for each cell $(i,j)$
\State Calculate the simulated reserve based on the simulated random variables for each cell $(i,j)$: $\tilde{R}^{*}=(\tilde{R}^{*}_{(1)},\tilde{R}^{*}_{(2)},...,\tilde{R}^{*}_{(N)})=(\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(1)}^{*},\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(2)}^{*},...,\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(N)}^{*})$
\State Calculate the empirical $75^{th}$ quantile of the $N$ simulated reserves for the ensemble: $R^{*}_{75}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Simulate $N$ random variables from $\text{Uniform}(0,1)$; Denote $\tilde{U}=(\tilde{U}_{(1)},...,\tilde{U}_{(N)})$ as the vector of $N$ simulated Uniformly distributed random variables
\State Denote $\tilde{Y}^{*}_{ij}=(\tilde{Y}^{*}_{ij,(1)},...,\tilde{Y}^{*}_{ij,(N)})$ as the vector of $N$ simulated variables for cell $(i,j)$ from the ensemble
\For{$n=1,..,N$}
\If{$\tilde{U}_{(n)} \in (\sum_{m=1}^{l-1}w_m,\sum_{m=1}^{l}w_m]$}
\State simulate a random variable from the $l^{th}$ component distribution, denoted as $\tilde{Y}_{ij}^{(l)}$
\State Set $\tilde{Y}^{*}_{ij,(n)}=\tilde{Y}_{ij}^{(l)}$
\EndIf
\EndFor
\State Repeat the above two steps for each cell $(i,j)$
\State Calculate the simulated reserve based on the simulated random variables for each cell $(i,j)$: $\tilde{R}^{*}=(\tilde{R}^{*}_{(1)},\tilde{R}^{*}_{(2)},...,\tilde{R}^{*}_{(N)})=(\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(1)}^{*},\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(2)}^{*},...,\sum_{i,j\in D^{out}}\tilde{Y}_{ij,(N)}^{*})$
\State Calculate the empirical $75^{th}$ quantile of the $N$ simulated reserves for the ensemble: $R^{*}_{75}$
\end{algorithmic} | "https://arxiv.org/src/2206.08541" | "2206.08541.tar.gz" | "2024-02-19" | {
"title": "ensemble distributional forecasting for insurance loss reserving",
"id": "2206.08541",
"abstract": "loss reserving generally focuses on identifying a single model that can generate superior predictive performance. however, different loss reserving models specialise in capturing different aspects of loss data. this is recognised in practice in the sense that results from different models are often considered, and sometimes combined. for instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. in this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple _stochastic_ loss reserving models such that the strengths offered by different models can be utilised effectively. our framework contains two main innovations compared to existing literature and practice. firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. secondly, our framework is that it is tailored for the features inherent to reserving data. these include, for instance, accident, development, calendar, and claim maturity effects. crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. our framework is illustrated with a complex synthetic dataset. in the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. in particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators).",
"categories": "stat.me q-fin.rm stat.ap",
"doi": "",
"created": "2022-06-17",
"updated": "2024-02-19",
"authors": [
"benjamin avanzi",
"yanfeng li",
"bernard wong",
"alan xian"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.08541"
} | "2024-03-15T03:14:29.396980" | {
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} | [] | "algorithm" | "1d289ead-1c69-4045-8011-bd2568d3d304" | 1151 | medium |
|
\begin{algorithmic}
\vspace{1mm}
\State{// \texttt{Iterate over all the haloes in catalogue}}
\For{ halo in catalogue }
\vspace{3mm}
\State{// \texttt{Compute probability of central}}
\State{$p_\text{cen} \leftarrow \text{model.}N_\text{cen}( $ halo.mass $ )$ }
\vspace{3mm}
\State{// \texttt{Define a binomial random variable}}
\State{select $\leftarrow$ random.Binomial(1, $p_\text{cen}$)}
\If{ select }
\State{halo $\leftarrow$ central}
\EndIf
\vspace{3mm}
\State{// \texttt{Compute average number of satellites}}
\State{$\overline{N}_\text{sat} \leftarrow \text{model.}N_\text{sat}( $ halo.mass $ )$}
\vspace{3mm}
\State{// \texttt{Define a Poisson random variable}}
\State{$N_\text{sat} = $ random.Poisson( $\overline{N}_\text{sat}$ )}
\State{halo $\leftarrow$ select randomly $N_\text{sat}$ objects among satellites}
\EndFor
\vspace{3mm}
\end{algorithmic}
| \begin{algorithmic}
\vspace{1mm}
\State{// \texttt{Iterate over all the haloes in catalogue}}
\For{ halo in catalogue }
\vspace{3mm}
\State{// \texttt{Compute probability of central}}
\State{$p_\text{cen} \leftarrow \text{model.}N_\text{cen}( $ halo.mass $ )$ }
\vspace{3mm}
\State{// \texttt{Define a binomial random variable}}
\State{select $\leftarrow$ random.Binomial(1, $p_\text{cen}$)}
\If{ select }
\State{halo $\leftarrow$ central}
\EndIf
\vspace{3mm}
\State{// \texttt{Compute average number of satellites}}
\State{$\overline{N}_\text{sat} \leftarrow \text{model.}N_\text{sat}( $ halo.mass $ )$}
\vspace{3mm}
\State{// \texttt{Define a Poisson random variable}}
\State{$N_\text{sat} = $ random.Poisson( $\overline{N}_\text{sat}$ )}
\State{halo $\leftarrow$ select randomly $N_\text{sat}$ objects among satellites}
\EndFor
\vspace{3mm}
\end{algorithmic} | "https://arxiv.org/src/2002.07179" | "2002.07179.tar.gz" | "2024-02-14" | {
"title": "scampy -- a sub-halo clustering & abundance matching based python interface for painting galaxies on the dark matter halo/sub-halo hierarchy",
"id": "2002.07179",
"abstract": "we present a computational framework for \"painting\" galaxies on top of the dark matter halo/sub-halo hierarchy obtained from n-body simulations. the method we use is based on the sub-halo clustering and abundance matching (scam) scheme which requires observations of the 1- and 2-point statistics of the target (observed) population we want to reproduce. this method is particularly tailored for high redshift studies and thereby relies on the observed high-redshift galaxy luminosity functions and correlation properties. the core functionalities are written in c++ and exploit object oriented programming, with a wide use of polymorphism, to achieve flexibility and high computational efficiency. in order to have an easily accessible interface, all the libraries are wrapped in python and provided with an extensive documentation. we validate our results and provide a simple and quantitative application to reionization, with an investigation of physical quantities related to the galaxy population, ionization fraction and bubble size distribution.",
"categories": "astro-ph.co",
"doi": "10.1093/mnras/staa2201",
"created": "2020-02-17",
"updated": "2024-02-14",
"authors": [
"tommaso ronconi",
"andrea lapi",
"matteo viel",
"alberto sartori"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2002.07179"
} | "2024-03-15T04:34:46.153353" | {
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} | [] | "algorithm" | "845af096-d4f2-4f54-96bd-5d99fe1e642a" | 861 | medium |
|
\begin{algorithmic}[1]
\Require $n \geq 0 \vee x \neq 0$
\Ensure $y = x^n$
\State $y \Leftarrow 1$
\If{$n < 0$}\label{algln2}
\State $X \Leftarrow 1 / x$
\State $N \Leftarrow -n$
\Else
\State $X \Leftarrow x$
\State $N \Leftarrow n$
\EndIf
\While{$N \neq 0$}
\If{$N$ is even}
\State $X \Leftarrow X \times X$
\State $N \Leftarrow N / 2$
\Else[$N$ is odd]
\State $y \Leftarrow y \times X$
\State $N \Leftarrow N - 1$
\EndIf
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require $n \geq 0 \vee x \neq 0$
\Ensure $y = x^n$
\State $y \Leftarrow 1$
\If{$n < 0$} \State $X \Leftarrow 1 / x$
\State $N \Leftarrow -n$
\Else
\State $X \Leftarrow x$
\State $N \Leftarrow n$
\EndIf
\While{$N \neq 0$}
\If{$N$ is even}
\State $X \Leftarrow X \times X$
\State $N \Leftarrow N / 2$
\Else[$N$ is odd]
\State $y \Leftarrow y \times X$
\State $N \Leftarrow N - 1$
\EndIf
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2312.05063" | "2312.05063.tar.gz" | "2024-02-25" | {
"title": "individualizing glioma radiotherapy planning by optimization of data and physics-informed discrete loss",
"id": "2312.05063",
"abstract": "brain tumor growth is unique to each patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. understanding these hidden patient-specific progressions is essential for effective therapies. current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. this \"one size fits all\" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. we present the framework gliodil which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging. this is achieved through the newly introduced method of optimizing the discrete loss (odil), where both data and physics-based constraints are softly assimilated into the solution. our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. by blending data-driven techniques with physics-based constraints adapted for complex cases, gliodil enhances recurrence prediction in radiotherapy planning, offering a superior alternative to traditional uniform margins and strict pde adherence.",
"categories": "physics.med-ph cs.na math.na q-bio.qm",
"doi": "",
"created": "2023-12-08",
"updated": "2024-02-25",
"authors": [
"michal balcerak",
"jonas weidner",
"petr karnakov",
"ivan ezhov",
"sergey litvinov",
"petros koumoutsakos",
"ray zirui zhang",
"john s. lowengrub",
"bene wiestler",
"bjoern menze"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.05063"
} | "2024-03-15T03:04:49.138400" | {
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} | [] | "algorithm" | "37f9ec91-081a-4799-9d19-7a6595228dc9" | 437 | easy |
|
\begin{algorithmic}[1]
\State Compute the set
\begin{equation*}
I(\mathbf{x}) = \left\{i \in \{1, \dots, N\} : \mathbf{x} \in \mathcal{B}_i\right\}.
\end{equation*}
\If{$|I(\mathbf{x})|=1$}
\State Assign $C(\mathbf{x})$ the unique element of $I(\mathbf{x})$.
\EndIf
\If{$|I(\mathbf{x})| = 0$}
\State $C(\mathbf{x}) = \arg\min_i d(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\If{$|I(\mathbf{x})| > 1$}
\State $C(\mathbf{x}) = \arg\min_i \tilde{d}(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Compute the set
\begin{equation*}
I(\mathbf{x}) = \left\{i \in \{1, \dots, N\} : \mathbf{x} \in \mathcal{B}_i\right\}.
\end{equation*}
\If{$|I(\mathbf{x})|=1$}
\State Assign $C(\mathbf{x})$ the unique element of $I(\mathbf{x})$.
\EndIf
\If{$|I(\mathbf{x})| = 0$}
\State $C(\mathbf{x}) = \arg\min_i d(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\If{$|I(\mathbf{x})| > 1$}
\State $C(\mathbf{x}) = \arg\min_i \tilde{d}(\mathbf{x},\mathcal{B}_i)$.
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2301.09734" | "2301.09734.tar.gz" | "2024-02-08" | {
"title": "topological learning in multi-class data sets",
"id": "2301.09734",
"abstract": "we specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. as a by-product, a topological classifier is defined that uses an open sub-covering of the data set. this sub-covering can be used to construct a simplicial complex whose topological features (e.g., betti numbers) provide information about the classification problem. we use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (dnns). we hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. we evaluate our topological classification algorithm on multiple constructed and open source data sets. we also validate our hypothesis regarding the relationship between topological complexity and learning in dnn's on multiple data sets.",
"categories": "cs.lg physics.data-an",
"doi": "",
"created": "2023-01-23",
"updated": "2024-02-08",
"authors": [
"christopher griffin",
"trevor karn",
"benjamin apple"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2301.09734"
} | "2024-03-15T05:24:48.442243" | {
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} | [] | "algorithm" | "be38228b-6714-4f2a-987e-5364b1359ad6" | 490 | easy |
|
\begin{algorithmic}
\State Initialize \(k=1, \mathbf{w}\sim Uniform(|\Phi|)\)
\While{\(k<k_{max}\)}
\State \(\hat{J}=-\infty\)
\For{\(\sigma_{\text{test}} \in [0,1]\)}
\If{\(J(\mathbf{w}, \sigma_{\text{test}}) > \hat{J}\)}
\State \(\sigma \gets \sigma_{\text{test}}\)
\State \(\hat{J} \gets J(\mathbf{w}, \sigma_{\text{test}})\)
\EndIf
\EndFor
\State Compute gradient \(\nabla_\mathbf{w} J(\mathbf{w},\sigma)\)
\State \(\mathbf{w} \gets \text{Proj}_{L_2}(\mathbf{w} - \alpha \nabla_\mathbf{w} J(\mathbf{w},\sigma))\)
\If{\(\left\|\nabla_\mathbf{w} J(\mathbf{w},\sigma) - \frac{\nabla_\mathbf{w} J(\mathbf{w},\sigma)^\top \mathbf{w}}{\|\mathbf{w}\|^2} \mathbf{w}\right\| < \beta\)}
\State terminate with \(\mathbf{w}\).
\EndIf
\State \(k\gets k+1\)
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
\State Initialize \(k=1, \mathbf{w}\sim Uniform(|\Phi|)\)
\While{\(k<k_{max}\)}
\State \(\hat{J}=-\infty\)
\For{\(\sigma_{\text{test}} \in [0,1]\)}
\If{\(J(\mathbf{w}, \sigma_{\text{test}}) > \hat{J}\)}
\State \(\sigma \gets \sigma_{\text{test}}\)
\State \(\hat{J} \gets J(\mathbf{w}, \sigma_{\text{test}})\)
\EndIf
\EndFor
\State Compute gradient \(\nabla_\mathbf{w} J(\mathbf{w},\sigma)\)
\State \(\mathbf{w} \gets \text{Proj}_{L_2}(\mathbf{w} - \alpha \nabla_\mathbf{w} J(\mathbf{w},\sigma))\)
\If{\(\left\|\nabla_\mathbf{w} J(\mathbf{w},\sigma) - \frac{\nabla_\mathbf{w} J(\mathbf{w},\sigma)^\top \mathbf{w}}{\|\mathbf{w}\|^2} \mathbf{w}\right\| < \beta\)}
\State terminate with \(\mathbf{w}\).
\EndIf
\State \(k\gets k+1\)
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2207.06392" | "2207.06392.tar.gz" | "2024-01-25" | {
"title": "relationship design for socially-aware behavior in static games",
"id": "2207.06392",
"abstract": "autonomous agents can adopt socially-aware behaviors to reduce social costs, mimicking the way animals interact in nature and humans in society. we present a new approach to model socially-aware decision-making that includes two key elements: bounded rationality and inter-agent relationships. we capture the interagent relationships by introducing a novel model called a relationship game and encode agents' bounded rationality using quantal response equilibria. for each relationship game, we define a social cost function and formulate a mechanism design problem to optimize weights for relationships that minimize social cost at the equilibrium. we address the multiplicity of equilibria by presenting the problem in two forms: min-max and min-min, aimed respectively at minimization of the highest and lowest social costs in the equilibria. we compute the quantal response equilibrium by solving a least-squares problem defined with its karush-kuhn-tucker conditions, and propose two projected gradient descent algorithms to solve the mechanism design problems. numerical results, including two-lane congestion and congestion with an ambulance, confirm that these algorithms consistently reach the equilibrium with the intended social costs.",
"categories": "cs.ma cs.sy eess.sy",
"doi": "",
"created": "2022-07-13",
"updated": "2024-01-25",
"authors": [
"shenghui chen",
"yigit e. bayiz",
"david fridovich-keil",
"ufuk topcu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.06392"
} | "2024-03-15T08:38:27.674079" | {
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} | [] | "algorithm" | "b6fcbba0-8428-4ca6-90b8-c0ab8babb1b1" | 775 | medium |
|
\begin{algorithm}[!ht]\caption{LSH, private procedures}\label{alg:LSH_private_app}
\begin{algorithmic}[1]
\State {\bf data structure} \textsc{LSH}
\State
\State {\bf private}
\Procedure{\textsc{ChooseHashFunc}}{$k,L\in \mathbb{N}_+$}\label{lin:choose_hash_func}
\For{$l \in [L]$}
\State \Comment{Amplify hash functions by concatenating}
\State $\mathcal{H}_{l} \leftarrow$ sample $k$ hash functions $(f_{1,l},f_{2,l},\cdots,f_{k,l})$ from $\mathcal{H}$ \label{lin:LSH_sample_k_functions}
\EndFor
\EndProcedure
\State
\Procedure{\textsc{ConstructHashTable}}{$\{x_i\}_{i\in[n]}\subset \mathbb{R}^d$}\label{lin:construct_hash_table}
\For{$l\in [L]$}
\For{$i\in [n]$}
\State $\mathcal{H}_l(x_i)$.\textsc{Insert}($x_i$) \label{lin:find_bucket_insert_element}
\State $\mathcal{T}_l\leftarrow \mathcal{T}_l\cup \mathcal{H}_l(x_i)$ \Comment{Creat hashtable by aggregating buckets} \label{lin:aggregate_hash_table}
\EndFor
\EndFor
\EndProcedure
\State {\bf end data structure}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}[!ht]
\caption{LSH, private procedures}\begin{algorithmic}
[1]
\State {\bf data structure} \textsc{LSH}
\State
\State {\bf private}
\Procedure{\textsc{ChooseHashFunc}}{$k,L\in \mathbb{N}_+$} \For{$l \in [L]$}
\State \Comment{Amplify hash functions by concatenating}
\State $\mathcal{H}_{l} \leftarrow$ sample $k$ hash functions $(f_{1,l},f_{2,l},\cdots,f_{k,l})$ from $\mathcal{H}$ \EndFor
\EndProcedure
\State
\Procedure{\textsc{ConstructHashTable}}{$\{x_i\}_{i\in[n]}\subset \mathbb{R}^d$} \For{$l\in [L]$}
\For{$i\in [n]$}
\State $\mathcal{H}_l(x_i)$.\textsc{Insert}($x_i$) \State $\mathcal{T}_l\leftarrow \mathcal{T}_l\cup \mathcal{H}_l(x_i)$ \Comment{Creat hashtable by aggregating buckets} \EndFor
\EndFor
\EndProcedure
\State {\bf end data structure}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2208.03915" | "2208.03915.tar.gz" | "2024-02-13" | {
"title": "dynamic maintenance of kernel density estimation data structure: from practice to theory",
"id": "2208.03915",
"abstract": "kernel density estimation (kde) stands out as a challenging task in machine learning. the problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\\{x_1, x_2, \\cdots, x_n \\} \\subset \\mathbb{r}^d$, we would like to compute $\\frac{1}{n}\\sum_{i=1}^{n} f(x_i,y)$ for any query point $y \\in \\mathbb{r}^d$. recently, there has been a growing trend of using data structures for efficient kde. however, the proposed kde data structures focus on static settings. the robustness of kde data structures over dynamic changing data distributions is not addressed. in this work, we focus on the dynamic maintenance of kde data structures with robustness to adversarial queries. especially, we provide a theoretical framework of kde data structures. in our framework, the kde data structures only require subquadratic spaces. moreover, our data structure supports the dynamic update of the dataset in sublinear time. furthermore, we can perform adaptive queries with the potential adversary in sublinear time.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2022-08-08",
"updated": "2024-02-13",
"authors": [
"jiehao liang",
"zhao song",
"zhaozhuo xu",
"junze yin",
"danyang zhuo"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2208.03915"
} | "2024-03-15T05:43:39.046127" | {
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} | [] | "algorithm" | "df723daa-5bbd-4dcf-a0b8-28a7b34143bd" | 808 | medium |
|
\begin{algorithmic}
\State $solutions \gets []$
\\ \Comment{Rule Generation}
\For{$k \gets 1, 2, 3, \ldots n$}
\If{$k = 1$}
\State $candidates \gets getNodeRules(model)$
\Else
\State $candidates \gets getNextStage(candidates, k)$
\EndIf
\\
\For{$r \gets candidates$}
\State $p \gets getPrecision(r \implies positiveLabel)$
\If{$p > 1 - \delta$}
\State $candidates.remove(r)$
\State $solutions.append(r)$
\EndIf
\EndFor
\EndFor
\\ \Comment{Rule Simplification}
\State $solutions \gets greedySetCover(solutions)$
\\
\Return $solutions$
\end{algorithmic}
| \begin{algorithmic}
\State $solutions \gets []$
\\ \Comment{Rule Generation}
\For{$k \gets 1, 2, 3, \ldots n$}
\If{$k = 1$}
\State $candidates \gets getNodeRules(model)$
\Else
\State $candidates \gets getNextStage(candidates, k)$
\EndIf
\\
\For{$r \gets candidates$}
\State $p \gets getPrecision(r \implies positiveLabel)$
\If{$p > 1 - \delta$}
\State $candidates.remove(r)$
\State $solutions.append(r)$
\EndIf
\EndFor
\EndFor
\\ \Comment{Rule Simplification}
\State $solutions \gets greedySetCover(solutions)$
\\
\Return $solutions$
\end{algorithmic} | "https://arxiv.org/src/2206.14359" | "2206.14359.tar.gz" | "2024-01-23" | {
"title": "te2rules: explaining tree ensembles using rules",
"id": "2206.14359",
"abstract": "tree ensemble (te) models, such as gradient boosted trees, often achieve optimal performance on tabular datasets, yet their lack of transparency poses challenges for comprehending their decision logic. this paper introduces te2rules (tree ensemble to rules), a novel approach for explaining binary classification tree ensemble models through a list of rules, particularly focusing on explaining the minority class. many state-of-the-art explainers struggle with minority class explanations, making te2rules valuable in such cases. the rules generated by te2rules closely approximate the original model, ensuring high fidelity, providing an accurate and interpretable means to understand decision-making. experimental results demonstrate that te2rules scales effectively to tree ensembles with hundreds of trees, achieving higher fidelity within runtimes comparable to baselines. te2rules allows for a trade-off between runtime and fidelity, enhancing its practical applicability. the implementation is available here: https://github.com/linkedin/te2rules.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2022-06-28",
"updated": "2024-01-23",
"authors": [
"g roshan lal",
"xiaotong chen",
"varun mithal"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.14359"
} | "2024-03-15T09:04:28.850184" | {
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} | [] | "algorithm" | "747ba3d5-8631-482c-94f1-e88f21f9e83d" | 551 | easy |
|
\begin{algorithmic}[1] % The number [1] indicates that lines are numbered
\Statex \textbf{Input:} Classifiers $h_0^*$ and $h_1^*$
\Statex \textbf{Output:} A randomized classifier $h^*_{\text{Fair}}:\mathcal{X}\times\{0,1\}\rightarrow\{0,1\}$
\State Compute $\alpha = \mathbb{P}_{\mu^X_0} (h^*_0(X) = 1 )$ and $\beta = \mathbb{P}_{\mu^X_1}(h^*_1(X) = 1 )$. W.L.O.G. assume $\alpha \geq \beta$
\State For $(x,a)$, randomly sample $s$ from the uniform distribution $U(0,1)$
\State Construct $h^*_{\text{Fair}}$ as follows:
\Statex $h_{\text {Fair }}^*(x, a):= \begin{cases}
a=0: & \begin{cases}0 & \text{if } h_0^*(x)=0 \text{ or } h_0^*(x)=1 \text{ and } s>\frac{\alpha+\beta}{2 \alpha} \\
1 & \text{if } h_0^*(x)=1 \text{ and } s \leq \frac{\alpha+\beta}{2 \alpha}\end{cases} \\
a=1: & \begin{cases}0 & \text{if } h_1^*(x)=0 \text{ and } s>\frac{\alpha-\beta}{2(1-\beta)} \\
1 & \text{if } h_1^*(x)=1 \text{ or } h_1^*(x)=0 \text{ and } s \leq \frac{\alpha-\beta}{2(1-\beta)}\end{cases}
\end{cases}$
\Statex \textbf{return} $h^*_{\text{Fair}}$
\end{algorithmic}
| \begin{algorithmic}[1]
% The number [1] indicates that lines are numbered
\Statex \textbf{Input:} Classifiers $h_0^*$ and $h_1^*$
\Statex \textbf{Output:} A randomized classifier $h^*_{\text{Fair}}:\mathcal{X}\times\{0,1\}\rightarrow\{0,1\}$
\State Compute $\alpha = \mathbb{P}_{\mu^X_0} (h^*_0(X) = 1 )$ and $\beta = \mathbb{P}_{\mu^X_1}(h^*_1(X) = 1 )$. W.L.O.G. assume $\alpha \geq \beta$
\State For $(x,a)$, randomly sample $s$ from the uniform distribution $U(0,1)$
\State Construct $h^*_{\text{Fair}}$ as follows:
\Statex $h_{\text {Fair }}^*(x, a):= \begin{cases}
a=0: & \begin{cases}
0 & \text{if } h_0^*(x)=0 \text{ or } h_0^*(x)=1 \text{ and } s>\frac{\alpha+\beta}{2 \alpha} \\
1 & \text{if } h_0^*(x)=1 \text{ and } s \leq \frac{\alpha+\beta}{2 \alpha}\end{cases} \\
a=1: & \begin{cases}
0 & \text{if } h_1^*(x)=0 \text{ and } s>\frac{\alpha-\beta}{2(1-\beta)} \\
1 & \text{if } h_1^*(x)=1 \text{ or } h_1^*(x)=0 \text{ and } s \leq \frac{\alpha-\beta}{2(1-\beta)}\end{cases}
\end{cases}$
\Statex \textbf{return} $h^*_{\text{Fair}}$
\end{algorithmic} | "https://arxiv.org/src/2402.15603" | "2402.15603.tar.gz" | "2024-02-23" | {
"title": "differentially private fair binary classifications",
"id": "2402.15603",
"abstract": "in this work, we investigate binary classification under the constraints of both differential privacy and fairness. we first propose an algorithm based on the decoupling technique for learning a classifier with only fairness guarantee. this algorithm takes in classifiers trained on different demographic groups and generates a single classifier satisfying statistical parity. we then refine this algorithm to incorporate differential privacy. the performance of the final algorithm is rigorously examined in terms of privacy, fairness, and utility guarantees. empirical evaluations conducted on the adult and credit card datasets illustrate that our algorithm outperforms the state-of-the-art in terms of fairness guarantees, while maintaining the same level of privacy and utility.",
"categories": "cs.lg cs.cr cs.it math.it stat.ml",
"doi": "",
"created": "2024-02-23",
"updated": "",
"authors": [
"hrad ghoukasian",
"shahab asoodeh"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.15603"
} | "2024-03-15T03:43:07.102159" | {
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} | [] | "algorithm" | "236edd78-153c-4be7-a691-f7c18995a882" | 1062 | medium |
|
\begin{algorithm}[tb]
\caption{Working Alliance Analysis (WAA)}
\label{alg:waa}
\begin{algorithmic}[1]
\State {\bfseries }\textbf{for} i = 1,2,$\cdots$, T \textbf{do}
\State {\bfseries } \quad Automatically transcribe dialogue turn pairs $(S^p_i,S^t_i)$
\State {\bfseries }\quad \textbf{for} $(I^p_j, I^t_j) \in$ inventories $(I^p, I^t)$ \textbf{do}
\State {\bfseries }\quad \quad Score $W^{p_i}_{j}$ = similarity($Emb({I^p_j}), Emb(S^p_i)$)
\State {\bfseries }\quad \quad Score $W^{t_i}_{j}$ = similarity($Emb({I^t_j}), Emb(S^t_i)$)
\State {\bfseries } \quad \textbf{end for}
\State {\bfseries } \textbf{end for}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[tb]
\caption{Working Alliance Analysis (WAA)}
\begin{algorithmic}
[1]
\State {\bfseries }\textbf{for} i = 1,2,$\cdots$, T \textbf{do}
\State {\bfseries } \quad Automatically transcribe dialogue turn pairs $(S^p_i,S^t_i)$
\State {\bfseries }\quad \textbf{for} $(I^p_j, I^t_j) \in$ inventories $(I^p, I^t)$ \textbf{do}
\State {\bfseries }\quad \quad Score $W^{p_i}_{j}$ = similarity($Emb({I^p_j}), Emb(S^p_i)$)
\State {\bfseries }\quad \quad Score $W^{t_i}_{j}$ = similarity($Emb({I^t_j}), Emb(S^t_i)$)
\State {\bfseries } \quad \textbf{end for}
\State {\bfseries } \textbf{end for}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.14701" | "2402.14701.tar.gz" | "2024-02-22" | {
"title": "compass: computational mapping of patient-therapist alliance strategies with language modeling",
"id": "2402.14701",
"abstract": "the therapeutic working alliance is a critical factor in predicting the success of psychotherapy treatment. traditionally, working alliance assessment relies on questionnaires completed by both therapists and patients. in this paper, we present compass, a novel framework to directly infer the therapeutic working alliance from the natural language used in psychotherapy sessions. our approach utilizes advanced large language models to analyze transcripts of psychotherapy sessions and compare them with distributed representations of statements in the working alliance inventory. analyzing a dataset of over 950 sessions covering diverse psychiatric conditions, we demonstrate the effectiveness of our method in microscopically mapping patient-therapist alignment trajectories and providing interpretability for clinical psychiatry and in identifying emerging patterns related to the condition being treated. by employing various neural topic modeling techniques in combination with generative language prompting, we analyze the topical characteristics of different psychiatric conditions and incorporate temporal modeling to capture the evolution of topics at a turn-level resolution. this combined framework enhances the understanding of therapeutic interactions, enabling timely feedback for therapists regarding conversation quality and providing interpretable insights to improve the effectiveness of psychotherapy.",
"categories": "cs.cl cs.ai cs.hc cs.lg q-bio.nc",
"doi": "",
"created": "2024-02-22",
"updated": "",
"authors": [
"baihan lin",
"djallel bouneffouf",
"yulia landa",
"rachel jespersen",
"cheryl corcoran",
"guillermo cecchi"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.14701"
} | "2024-03-15T03:21:50.438155" | {
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} | [] | "algorithm" | "a010c2b9-6ba2-4b65-b5c3-2c168747e932" | 633 | easy |
|
\begin{algorithmic}
\State \textbf{Input:} Independent initial samples $x_1^{(0)},...,x_N^{(0)}$ from $\mu_0$, momentum parameters $m_l\in[0,1)$ for $l=1,...,L$.
\State Initialize $(v_1,...,v_N)=0$.
\For{$l=1,...,L$}
\State - Set $(\tilde x_1^{(0)},...,\tilde x_N^{(0)})=(x_1^{(l-1)},...,x_N^{(l-1)})$.
\State - Simulate $T_l$ steps of the (momentum) MMD flow:
\For{$t=1,...,T_l$}
\State - Update $v$ by
\begin{align*}
(v_1,...,v_N)\leftarrow \nabla F_d(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)}|y_1,...,y_M)+m_l (v_1,...,v_N)
\end{align*}
\State - Update the flow samples:
\begin{align*}
(\tilde x_1^{(t)},...,\tilde x_N^{(t)})=(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)})-\tau N\ (v_1,...,v_N)
\end{align*}
\EndFor
\State - Train $\Phi_l$ such that $\tilde x^{(T_l)}\approx \tilde x_i^{(0)}-\Phi_l(\tilde x_i^{(0)}) $ by minimizing the loss
\begin{align*}
\mathcal L(\theta_l)=\frac1N\sum_{i=1}^N \|\Phi_l(\tilde x_i^{(0)})-(\tilde x_i^{(0)}-\tilde x_i^{(T_l)})\|^2.
\end{align*}
\State - Set $(x_1^{(l)},...,x_N^{(l)})=(x_1^{(l-1)},...,x_N^{(l-1)})-(\Phi_l(x_1^{(l-1)}),...,\Phi_l(x_N^{(l-1)}))$.
\EndFor
\end{algorithmic}
| \begin{algorithmic}
\State \textbf{Input:} Independent initial samples $x_1^{(0)},...,x_N^{(0)}$ from $\mu_0$, momentum parameters $m_l\in[0,1)$ for $l=1,...,L$.
\State Initialize $(v_1,...,v_N)=0$.
\For{$l=1,...,L$}
\State - Set $(\tilde x_1^{(0)},...,\tilde x_N^{(0)})=(x_1^{(l-1)},...,x_N^{(l-1)})$.
\State - Simulate $T_l$ steps of the (momentum) MMD flow:
\For{$t=1,...,T_l$}
\State - Update $v$ by
\begin{align*}
(v_1,...,v_N)\leftarrow \nabla F_d(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)}|y_1,...,y_M)+m_l (v_1,...,v_N)
\end{align*}
\State - Update the flow samples:
\begin{align*}
(\tilde x_1^{(t)},...,\tilde x_N^{(t)})=(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)})-\tau N\ (v_1,...,v_N)
\end{align*}
\EndFor
\State - Train $\Phi_l$ such that $\tilde x^{(T_l)}\approx \tilde x_i^{(0)}-\Phi_l(\tilde x_i^{(0)}) $ by minimizing the loss
\begin{align*}
\mathcal L(\theta_l)=\frac1N\sum_{i=1}^N \|\Phi_l(\tilde x_i^{(0)})-(\tilde x_i^{(0)}-\tilde x_i^{(T_l)})\|^2.
\end{align*}
\State - Set $(x_1^{(l)},...,x_N^{(l)})=(x_1^{(l-1)},...,x_N^{(l-1)})-(\Phi_l(x_1^{(l-1)}),...,\Phi_l(x_N^{(l-1)}))$.
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2305.11463" | "2305.11463.tar.gz" | "2024-02-20" | {
"title": "generative sliced mmd flows with riesz kernels",
"id": "2305.11463",
"abstract": "maximum mean discrepancy (mmd) flows suffer from high computational costs in large scale computations. in this paper, we show that mmd flows with riesz kernels $k(x,y) = - \\|x-y\\|^r$, $r \\in (0,2)$ have exceptional properties which allow their efficient computation. we prove that the mmd of riesz kernels, which is also known as energy distance, coincides with the mmd of their sliced version. as a consequence, the computation of gradients of mmds can be performed in the one-dimensional setting. here, for $r=1$, a simple sorting algorithm can be applied to reduce the complexity from $o(mn+n^2)$ to $o((m+n)\\log(m+n))$ for two measures with $m$ and $n$ support points. as another interesting follow-up result, the mmd of compactly supported measures can be estimated from above and below by the wasserstein-1 distance. for the implementations we approximate the gradient of the sliced mmd by using only a finite number $p$ of slices. we show that the resulting error has complexity $o(\\sqrt{d/p})$, where $d$ is the data dimension. these results enable us to train generative models by approximating mmd gradient flows by neural networks even for image applications. we demonstrate the efficiency of our model by image generation on mnist, fashionmnist and cifar10.",
"categories": "cs.lg math.pr stat.ml",
"doi": "",
"created": "2023-05-19",
"updated": "2024-02-20",
"authors": [
"johannes hertrich",
"christian wald",
"fabian altekr\u00fcger",
"paul hagemann"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2305.11463"
} | "2024-03-15T04:32:53.456595" | {
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} | [] | "algorithm" | "078ffa9b-811e-4152-aa26-00a8190564a6" | 1124 | medium |
|
\begin{algorithm}\label{alg:sbo2}
An equivalent formulation to Algorithm \ref{alg:sbo1} is to (i) scramble $A$ and map it onto an ordered set, then (ii) order the scrambled blocks by least element. Let $\sigma:A\to\{1,\dots,n\}$ be a uniform random bijection and order the blocks in increasing order of $\min \sigma(B)$ as $(B_i)_{i=1}^\ell$. Then $u(i):=\sigma^{-1}(i)$ and $I_i:=\min \sigma(B_i)$ are exactly as in Algorithm \ref{alg:sbo1}, i.e., $(B_i)_{i=1}^\ell$ is a size-biased ordering of $P$.
\end{algorithm}
| \begin{algorithm}
An equivalent formulation to Algorithm \ref{alg:sbo1} is to (i) scramble $A$ and map it onto an ordered set, then (ii) order the scrambled blocks by least element. Let $\sigma:A\to\{1,\dots,n\}$ be a uniform random bijection and order the blocks in increasing order of $\min \sigma(B)$ as $(B_i)_{i=1}^\ell$. Then $u(i):=\sigma^{-1}(i)$ and $I_i:=\min \sigma(B_i)$ are exactly as in Algorithm \ref{alg:sbo1}, i.e., $(B_i)_{i=1}^\ell$ is a size-biased ordering of $P$.
\end{algorithm} | "https://arxiv.org/src/2104.00193" | "2104.00193.tar.gz" | "2024-01-12" | {
"title": "takeover, fixation and identifiability in finite neutral genealogy models",
"id": "2104.00193",
"abstract": "for neutral genealogy models in a finite, possibly non-constant population, there is a convenient ordered rearrangement of the particles, known as the lookdown representation, that greatly simplifies the analysis of the family trees. by introducing the dual notions of forward and backward neutrality, we give a more intuitive implementation of this rearrangement. we also show that the lookdown arranges subtrees in size-biased order of the number of their descendants, a property that is familiar in other settings but appears not to have been previously established in this context. in addition, we use the lookdown to study three properties of finite neutral models, as a function of the sequence of unlabelled litter sizes of the model: uniqueness of the infinite path (fixation), existence of a single lineage to which almost all individuals can trace their ancestry (takeover) and whether or not we can infer the lookdown rearrangement by examining the unlabelled genealogy model (identifiability). identifiability of the spine path in size-biased galton-watson trees was previously studied, so we also discuss connections to those results, by relating the spinal decomposition to the lookdown.",
"categories": "math.pr",
"doi": "",
"created": "2021-03-31",
"updated": "2024-01-12",
"authors": [
"eric foxall",
"jen labossiere"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2104.00193"
} | "2024-03-15T06:08:13.487657" | {
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} | [] | "algorithm" | "4c89b80b-8597-4535-a477-f7125e3c7c7f" | 501 | easy |
|
\begin{algorithm}
\caption{Dynamics-based Arrival Date Computation}\label{alg:variant_arrival}
\begin{algorithmic}[1]
\ForAll{$X_p$ in $\{X_1, X_2, \dots\}_t$}
\State Calculate and store delay predictions for $(X_p, Y)$ until the current date, $t$.
\EndFor
\If{$t \neq 0$}
\State Select top 3 $X_p$ with the best performance at $t-1$
\Else
\State Select all source regions $\{X_1, X_2, \dots\}_t$
\EndIf
\State Find the median of delay predictions for selected models
\State \textbf{return} Median delay as the estimated arrival date for the variant in region $Y$ at time $t$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Dynamics-based Arrival Date Computation} \begin{algorithmic}
[1]
\ForAll{$X_p$ in $\{X_1, X_2, \dots\}_t$}
\State Calculate and store delay predictions for $(X_p, Y)$ until the current date, $t$.
\EndFor
\If{$t \neq 0$}
\State Select top 3 $X_p$ with the best performance at $t-1$
\Else
\State Select all source regions $\{X_1, X_2, \dots\}_t$
\EndIf
\State Find the median of delay predictions for selected models
\State \textbf{return} Median delay as the estimated arrival date for the variant in region $Y$ at time $t$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.03390" | "2401.03390.tar.gz" | "2024-01-07" | {
"title": "global prediction of covid-19 variant emergence using dynamics-informed graph neural networks",
"id": "2401.03390",
"abstract": "during the covid-19 pandemic, a major driver of new surges has been the emergence of new variants. when a new variant emerges in one or more countries, other nations monitor its spread in preparation for its potential arrival. the impact of the variant and the timing of epidemic peaks in a country highly depend on when the variant arrives. the current methods for predicting the spread of new variants rely on statistical modeling, however, these methods work only when the new variant has already arrived in the region of interest and has a significant prevalence. the question arises: can we predict when (and if) a variant that exists elsewhere will arrive in a given country and reach a certain prevalence? we propose a variant-dynamics-informed graph neural network (gnn) approach. first, we derive the dynamics of variant prevalence across pairs of regions (countries) that applies to a large class of epidemic models. the dynamics suggest that ratios of variant proportions lead to simpler patterns. therefore, we use ratios of variant proportions along with some parameters estimated from the dynamics as features in a gnn. we develop a benchmarking tool to evaluate variant emergence prediction over 87 countries and 36 variants. we leverage this tool to compare our gnn-based approach against our dynamics-only model and a number of machine learning models. results show that the proposed dynamics-informed gnn method retrospectively outperforms all the baselines, including the currently pervasive framework of physics-informed neural networks (pinns) that incorporates the dynamics in the loss function.",
"categories": "q-bio.pe cs.lg physics.soc-ph",
"doi": "",
"created": "2024-01-07",
"updated": "",
"authors": [
"majd al aawar",
"srikar mutnuri",
"mansooreh montazerin",
"ajitesh srivastava"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.03390"
} | "2024-03-15T07:51:28.358213" | {
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} | [] | "algorithm" | "5fcefa49-ac51-47dc-af4d-df5297782c70" | 583 | easy |
|
\begin{algorithm}
\caption{Conventional Screening Applied to Graphs}
\label{alg:vs}
\begin{algorithmic}[1]
\Require{$\{(A_i,Y_i)\}_{i=1}^m$ and $c \in [0,1]$}{}
\For{$u \in V$ }
\State $X_i=A_{i}[u,\cdot]$
\State $\beta(u) = Dcor(\{X_i, Y_i\}_{i=1}^m )$
\EndFor
\State $\hat{S} = \{u \in V| \beta(u) > c\}$.
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Conventional Screening Applied to Graphs}
\begin{algorithmic}
[1]
\Require{$\{(A_i,Y_i)\}_{i=1}^m$ and $c \in [0,1]$}{}
\For{$u \in V$ }
\State $X_i=A_{i}[u,\cdot]$
\State $\beta(u) = Dcor(\{X_i, Y_i\}_{i=1}^m )$
\EndFor
\State $\hat{S} = \{u \in V| \beta(u) > c\}$.
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/1801.07683" | "1801.07683.tar.gz" | "2024-02-05" | {
"title": "discovering the signal subgraph: an iterative screening approach on graphs",
"id": "1801.07683",
"abstract": "supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. existing conventional methods designed for euclidean data do not account for this graph dependency structure. to address this issue, this paper proposes an iterative vertex screening method to identify the signal subgraph that is most informative for the given graph attributes. the method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. we establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. additionally, we establish the convergence rate of classification error under the erdos-renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. the results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.",
"categories": "stat.me",
"doi": "",
"created": "2018-01-23",
"updated": "2024-02-05",
"authors": [
"cencheng shen",
"shangsi wang",
"alexandra badea",
"carey e. priebe",
"joshua t. vogelstein"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1801.07683"
} | "2024-03-15T06:55:05.801196" | {
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} | [] | "algorithm" | "cc1b7c4e-d7c2-4dc0-bb8f-d35405db8b74" | 327 | easy |
|
\begin{algorithm}
\caption{Modified Gradient Descent with Triggering Events}
\label{alg:inner loop}
\begin{algorithmic}[1]
\Procedure{ModifiedGD}{$\nabla F, \hat{L}_{i, 0}, \delta_{(i, \cdot)}, R, \theta_{i, 0}, \kappa_{(i,\cdot)}, T^*, \ell, \gamma$}
\State $ \Delta \leftarrow 0 $ \Comment{Measure of predicted decrease of objective}
\For{$j = 0, 1, ..., T^*-1$}
\State $\alpha_{i,j} \leftarrow \delta_{(i,\cdot)} (2||\nabla F(\theta_{i,j})||^3 + ||\nabla F(\theta_{i,j})||^2\hat{L}_{i,j} )^{-1}$ \Comment{Step size computation}
\State $\theta_{i, j+1} \leftarrow \theta_{i,j} - \alpha_{i,j} \nabla F(\theta_{i,j})$ \Comment{Gradient step}
\State $\Delta \leftarrow \Delta - \delta_{(i,\cdot)}^2\left( 4||\nabla F(\theta_{i,j})||^3 + 2\hat{L}_{i,j}||\nabla F(\theta_{i,j}) ||^2 \right)^{-1}$ \Comment{Update predicted decrease}
\If{ $|| \theta_{i,j} - \theta_{i,j+1} || \ge 10^{-10}$ }
\State $\hat{L}_{i,j+1} \leftarrow \Call{UpdateL}{\nabla F, \theta_{i,j}, \theta_{i,j+1}, \hat{L}_{i,j}, \kappa_{(i,\cdot)}, \ell}$ \Comment{Update local Lipschitz estimate}
\Else
\State $\hat{L}_{i,j+1} \leftarrow \hat{L}_{i,j}$
\EndIf
\State $ \delta_{cond} \leftarrow ||\nabla F(\theta_{i,j+1})||^2 \not\in (\delta_{(i,\cdot)}, \gamma\delta_{(i,\cdot)})$
\If{$\delta_{cond}$ or $||\theta_{i,j+1}-\theta_{i,0}|| > R$ or stop condition} \Comment{Check triggering events}
\State \Return{$\theta_{i,j+1},\hat{L}_{i,j+1},\delta_{cond},\Delta$}
\EndIf
\EndFor
\State
\Return{$\theta_{i,T^*},\hat{L}_{i,T^*},\delta_{cond},\Delta$}
\EndProcedure
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Modified Gradient Descent with Triggering Events}
\begin{algorithmic}
[1]
\Procedure{ModifiedGD}{$\nabla F, \hat{L}_{i, 0}, \delta_{(i, \cdot)}, R, \theta_{i, 0}, \kappa_{(i,\cdot)}, T^*, \ell, \gamma$}
\State $ \Delta \leftarrow 0 $ \Comment{Measure of predicted decrease of objective}
\For{$j = 0, 1, ..., T^*-1$}
\State $\alpha_{i,j} \leftarrow \delta_{(i,\cdot)} (2||\nabla F(\theta_{i,j})||^3 + ||\nabla F(\theta_{i,j})||^2\hat{L}_{i,j} )^{-1}$ \Comment{Step size computation}
\State $\theta_{i, j+1} \leftarrow \theta_{i,j} - \alpha_{i,j} \nabla F(\theta_{i,j})$ \Comment{Gradient step}
\State $\Delta \leftarrow \Delta - \delta_{(i,\cdot)}^2\left( 4||\nabla F(\theta_{i,j})||^3 + 2\hat{L}_{i,j}||\nabla F(\theta_{i,j}) ||^2 \right)^{-1}$ \Comment{Update predicted decrease}
\If{ $|| \theta_{i,j} - \theta_{i,j+1} || \ge 10^{-10}$ }
\State $\hat{L}_{i,j+1} \leftarrow \Call{UpdateL}{\nabla F, \theta_{i,j}, \theta_{i,j+1}, \hat{L}_{i,j}, \kappa_{(i,\cdot)}, \ell}$ \Comment{Update local Lipschitz estimate}
\Else
\State $\hat{L}_{i,j+1} \leftarrow \hat{L}_{i,j}$
\EndIf
\State $ \delta_{cond} \leftarrow ||\nabla F(\theta_{i,j+1})||^2 \not\in (\delta_{(i,\cdot)}, \gamma\delta_{(i,\cdot)})$
\If{$\delta_{cond}$ or $||\theta_{i,j+1}-\theta_{i,0}|| > R$ or stop condition} \Comment{Check triggering events}
\State \Return{$\theta_{i,j+1},\hat{L}_{i,j+1},\delta_{cond},\Delta$}
\EndIf
\EndFor
\State
\Return{$\theta_{i,T^*},\hat{L}_{i,T^*},\delta_{cond},\Delta$}
\EndProcedure
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2309.10894" | "2309.10894.tar.gz" | "2024-02-15" | {
"title": "a novel gradient methodology with economical objective function evaluations for data science applications",
"id": "2309.10894",
"abstract": "gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges of optimization problems arising in data science. focusing on data science applications with expensive objective function evaluations yet inexpensive gradient function evaluations, gradient methods that never make objective function evaluations are either being rejuvenated or actively developed. however, as we show, such gradient methods are all susceptible to catastrophic divergence under realistic conditions for data science applications. in light of this, gradient methods which make use of objective function evaluations become more appealing, yet, as we show, can result in an exponential increase in objective evaluations between accepted iterates. as a result, existing gradient methods are poorly suited to the needs of optimization problems arising from data science. in this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent catastrophic divergence and avoid an explosion in objective evaluations between accepted iterates. our methodology allows for specific procedures that can make use of specific step size selection methodologies or search direction strategies, and we develop a novel step size selection methodology that is well-suited to data science applications. we show that a procedure resulting from our methodology is highly competitive with standard optimization methods on cutest test problems. we then show a procedure resulting from our methodology is highly favorable relative to standard optimization methods on optimization problems arising in our target data science applications. thus, we provide a novel gradient methodology that is better suited to optimization problems arising in data science.",
"categories": "math.oc stat.co",
"doi": "",
"created": "2023-09-19",
"updated": "2024-02-15",
"authors": [
"christian varner",
"vivak patel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2309.10894"
} | "2024-03-15T05:06:27.333458" | {
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} | [] | "algorithm" | "c86adc1c-d642-421b-84bd-bb24d2165239" | 1540 | hard |
|
\begin{algorithm}[htb]
\caption{Mixed precision variant of LSQR for \eqref{1.1}}\label{alg3}
\begin{algorithmic}[1]
\Require $A$, $b$, $x_{0}=\mathbf{0}$
\For{$k=1,2,\ldots,$}
\State Compute $p_k$, $q_k$, $\alpha_k$, $\beta_k$ by the LBFRO \algorithmiccomment{roundoff unit is $\mathbf{u}$}
\State Compute $\rho_k$, $\theta_{k+1}$, $\bar{\rho}_{k+1}$, $\phi_{k}$, $\bar{\phi}_{k+1}$ by the updating procedure \algorithmiccomment{double precision}
\State Compute $x_k$, $w_{k+1}$ by the updating procedure \algorithmiccomment{roundoff unit is $\mathbf{\bar{u}}$}
\If{Early stopping criterion is satisfied} \algorithmiccomment{DP or L-curve criterion}
\State The semi-convergence point is estimated as $k_1$
\State Terminate the iteration
\EndIf
\EndFor
\Ensure Final regularized solution $\hat{x}_{k_1}$ \algorithmiccomment{Computed solution corresponding to $x_{k_1}$}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[htb]
\caption{Mixed precision variant of LSQR for \eqref{1.1}} \begin{algorithmic}
[1]
\Require $A$, $b$, $x_{0}=\mathbf{0}$
\For{$k=1,2,\ldots,$}
\State Compute $p_k$, $q_k$, $\alpha_k$, $\beta_k$ by the LBFRO \algorithmiccomment{roundoff unit is $\mathbf{u}$}
\State Compute $\rho_k$, $\theta_{k+1}$, $\bar{\rho}_{k+1}$, $\phi_{k}$, $\bar{\phi}_{k+1}$ by the updating procedure \algorithmiccomment{double precision}
\State Compute $x_k$, $w_{k+1}$ by the updating procedure \algorithmiccomment{roundoff unit is $\mathbf{\bar{u}}$}
\If{Early stopping criterion is satisfied} \algorithmiccomment{DP or L-curve criterion}
\State The semi-convergence point is estimated as $k_1$
\State Terminate the iteration
\EndIf
\EndFor
\Ensure Final regularized solution $\hat{x}_{k_1}$ \algorithmiccomment{Computed solution corresponding to $x_{k_1}$}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2210.11025" | "2210.11025.tar.gz" | "2024-02-12" | {
"title": "double precision is not necessary for lsqr for solving discrete linear ill-posed problems",
"id": "2210.11025",
"abstract": "the growing availability and usage of low precision foating point formats has attracts many interests of developing lower or mixed precision algorithms for scientific computing problems. in this paper we investigate the possibility of exploiting lower precision computing in lsqr for solving discrete linear ill-posed problems. we analyze the choice of proper computing precisions in the two main parts of lsqr, including the construction of lanczos vectors and updating procedure of iterative solutions. we show that, under some mild conditions, the lanczos vectors can be computed using single precision without loss of any accuracy of final regularized solutions as long as the noise level is not extremely small. we also show that the most time consuming part for updating iterative solutions can be performed using single precision without sacrificing any accuracy. the results indicate that the most time consuming parts of the algorithm can be implemented using single precision, and thus the performance of lsqr for solving discrete linear ill-posed problems can be significantly enhanced. numerical experiments are made for testing the single precision variants of lsqr and confirming our results.",
"categories": "math.na cs.na",
"doi": "10.1007/s10915-023-02447-4",
"created": "2022-10-20",
"updated": "2024-02-12",
"authors": [
"haibo li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.11025"
} | "2024-03-15T06:22:07.329432" | {
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} | [] | "algorithm" | "83abbcf3-a319-4f9d-ae9e-68b6ef556a1f" | 892 | medium |
|
\begin{algorithmic}[1]
\State Perform Step 1 - 3 proposed in \textbf{Algorithm} \ref{alg:EFT}. Based on $\{\check{\Lambda}_{\mathbf{C}}(t_j)\}_{ j =1}^n$, obtain the Jackknife bias-corrected estimators $T_n(t) = \check{\Lambda}_{\mathbf{C}}(t) - f(t, \{\check{\Lambda}_{\mathbf{C}}(v_i)\}_{i =1}^k)$, and construct the corresponding bootstrap statistics $\{\check{L}^{(r)}_n(t) = \tilde{\boldsymbol{\Phi}}^{(r)}_n (t) - \sum_{j =1}^k\partial_j f(t, \{\check{\Lambda}_{\mathbf{C}}(v_i)\}_{i =1}^k)\tilde{\boldsymbol{\Phi}}^{(r)}_n (v_j)\}_{r = 1}^B$.
\State Calculate $M_r =\max_{i_* \le j \le i^*} |\check{L}^{(r)}_n(t_j)|_\infty$, $r=1,2,\cdots,B$.
\State For a given $\alpha \in (0,1)$, find the $(1-\alpha)$-th sample quantile of $\{M_r\}_{r=1}^B$, $\hat{q}_{n,1-\alpha}$.
\State For the Lack-of-fit Test $H_0: \Lambda_{\mathbf{C}}(t) - f(t, \{\Lambda_{\mathbf{C}}(t_i)\}_{i =1}^k) = \mathbf{0}, \quad t \in (0,1)$, reject the null hypothesis if $ \max_{i_* \le j \le i^*}|T_n(t_j)|_\infty > \hat{q}_{n,1-\alpha}/\sqrt{n}$.
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Perform Step 1 - 3 proposed in \textbf{Algorithm} \ref{alg:EFT}. Based on $\{\check{\Lambda}_{\mathbf{C}}(t_j)\}_{ j =1}^n$, obtain the Jackknife bias-corrected estimators $T_n(t) = \check{\Lambda}_{\mathbf{C}}(t) - f(t, \{\check{\Lambda}_{\mathbf{C}}(v_i)\}_{i =1}^k)$, and construct the corresponding bootstrap statistics $\{\check{L}^{(r)}_n(t) = \tilde{\boldsymbol{\Phi}}^{(r)}_n (t) - \sum_{j =1}^k\partial_j f(t, \{\check{\Lambda}_{\mathbf{C}}(v_i)\}_{i =1}^k)\tilde{\boldsymbol{\Phi}}^{(r)}_n (v_j)\}_{r = 1}^B$.
\State Calculate $M_r =\max_{i_* \le j \le i^*} |\check{L}^{(r)}_n(t_j)|_\infty$, $r=1,2,\cdots,B$.
\State For a given $\alpha \in (0,1)$, find the $(1-\alpha)$-th sample quantile of $\{M_r\}_{r=1}^B$, $\hat{q}_{n,1-\alpha}$.
\State For the Lack-of-fit Test $H_0: \Lambda_{\mathbf{C}}(t) - f(t, \{\Lambda_{\mathbf{C}}(t_i)\}_{i =1}^k) = \mathbf{0}, \quad t \in (0,1)$, reject the null hypothesis if $ \max_{i_* \le j \le i^*}|T_n(t_j)|_\infty > \hat{q}_{n,1-\alpha}/\sqrt{n}$.
\end{algorithmic} | "https://arxiv.org/src/2310.11724" | "2310.11724.tar.gz" | "2024-02-26" | {
"title": "simultaneous nonparametric inference of m-regression under complex temporal dynamics",
"id": "2310.11724",
"abstract": "the paper considers simultaneous nonparametric inference for a wide class of m-regression models with time-varying coefficients. the covariates and errors of the regression model are tackled as a general class of nonstationary time series and are allowed to be cross-dependent. we construct $\\sqrt{n}$-consistent inference for the cumulative regression function, whose limiting properties are disclosed using bahadur representation and gaussian approximation theory. a simple and unified self-convolved bootstrap procedure is proposed. with only one tuning parameter, the bootstrap consistently simulates the desired limiting behavior of the m-estimators under complex temporal dynamics, even under the possible presence of breakpoints in time series. our methodology leads to a unified framework to conduct general classes of exact function tests, lack-of-fit tests, and qualitative tests for the time-varying coefficients under complex temporal dynamics. these tests enable one to, among many others, conduct variable selection procedures, check for constancy and linearity, as well as verify shape assumptions, including monotonicity and convexity. as applications, our method is utilized to study the time-varying properties of global climate data and microsoft stock return, respectively.",
"categories": "stat.me math.st stat.th",
"doi": "",
"created": "2023-10-18",
"updated": "2024-02-26",
"authors": [
"miaoshiqi liu",
"zhou zhou"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.11724"
} | "2024-03-15T03:19:25.303660" | {
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\begin{algorithm}
\caption{The market return fitting step in training GF-AGRU.} \label{algorithm_N}
\textbf{Hyperparameters}: learning rate $l_{\text{fix}}$ of the FIX-OPTIM sub-procedure, learning rate $l_{\text{tv}}$ of the TV-AGRU sub-procedure, number of maximum iterative steps $N_m$, number of training epochs $N_{\text{fix}}$ of FIX-OPTIM, number of training epochs $N_{\text{tv}}$ of TV-AGRU, and the training set size $S$.\\
\textbf{Input}: training data including the features $F_{<t}$ and the label $Y_M^t$. $F_{<t}$ is constructed by Equation \eqref{eqn:features_Ft} using historical daily market returns, and $Y_M^t$ is the future one-month return. The training set collects data points on a daily frequency. \\
\textbf{Initialize}: tail parameters $\nu_M=\{u_M,v_M\}$ and the Attention-GRU network parameters $\theta_{\text{AGRU}}$.
\begin{algorithmic}[1]
\For{$b=1:N_m$}
\State (TV-AGRU)
\State Fix $\nu_M$ given by FIX-OPTIM.
\For{$j=1:N_{\text{tv}}$}
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$.
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\theta_{\text{AGRU}}$.
\State Update: $\theta_{\text{AGRU}} \gets \text{RMSProp}(\theta_{\text{AGRU}},\nabla_{\theta_{\text{AGRU}}} L,l_{\text{tv}})$.
\EndFor
\State (FIX-OPTIM)
\State Fix $\theta_{\text{AGRU}}$ given by TV-AGRU.
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$ and fix $\Theta^t_M$.
\For{$j=1:N_{\text{fix}}$}
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\nu_M$.
\State Update: $\nu_M \gets \text{RMSProp}(\nu_M,\nabla_{\nu_M} L,l_{\text{fix}})$.
\EndFor
\EndFor
\end{algorithmic}
\textbf{Output}: learnable parameters $\nu_M$ and $\theta_{\text{AGRU}}$; the time-varying model parameters $\Theta^t_M$; the realized latent market factor $\tilde{Z}_M^t$ given by Equation (\ref{latentfac}).
\end{algorithm}
| \begin{algorithm}
\caption{The market return fitting step in training GF-AGRU.} \textbf{Hyperparameters}: learning rate $l_{\text{fix}}$ of the FIX-OPTIM sub-procedure, learning rate $l_{\text{tv}}$ of the TV-AGRU sub-procedure, number of maximum iterative steps $N_m$, number of training epochs $N_{\text{fix}}$ of FIX-OPTIM, number of training epochs $N_{\text{tv}}$ of TV-AGRU, and the training set size $S$.\\
\textbf{Input}: training data including the features $F_{<t}$ and the label $Y_M^t$. $F_{<t}$ is constructed by Equation \eqref{eqn:features_Ft} using historical daily market returns, and $Y_M^t$ is the future one-month return. The training set collects data points on a daily frequency. \\
\textbf{Initialize}: tail parameters $\nu_M=\{u_M,v_M\}$ and the Attention-GRU network parameters $\theta_{\text{AGRU}}$.
\begin{algorithmic}
[1]
\For{$b=1:N_m$}
\State (TV-AGRU)
\State Fix $\nu_M$ given by FIX-OPTIM.
\For{$j=1:N_{\text{tv}}$}
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$.
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\theta_{\text{AGRU}}$.
\State Update: $\theta_{\text{AGRU}} \gets \text{RMSProp}(\theta_{\text{AGRU}},\nabla_{\theta_{\text{AGRU}}} L,l_{\text{tv}})$.
\EndFor
\State (FIX-OPTIM)
\State Fix $\theta_{\text{AGRU}}$ given by TV-AGRU.
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$ and fix $\Theta^t_M$.
\For{$j=1:N_{\text{fix}}$}
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\nu_M$.
\State Update: $\nu_M \gets \text{RMSProp}(\nu_M,\nabla_{\nu_M} L,l_{\text{fix}})$.
\EndFor
\EndFor
\end{algorithmic}
\textbf{Output}: learnable parameters $\nu_M$ and $\theta_{\text{AGRU}}$; the time-varying model parameters $\Theta^t_M$; the realized latent market factor $\tilde{Z}_M^t$ given by Equation (\ref{latentfac}).
\end{algorithm} | "https://arxiv.org/src/2301.07318" | "2301.07318.tar.gz" | "2024-01-16" | {
"title": "dynamic cvar portfolio construction with attention-powered generative factor learning",
"id": "2301.07318",
"abstract": "the dynamic portfolio construction problem requires dynamic modeling of the joint distribution of multivariate stock returns. to achieve this, we propose a dynamic generative factor model which uses random variable transformation as an implicit way of distribution modeling and relies on the attention-gru network for dynamic learning and forecasting. the proposed model captures the dynamic dependence among multivariate stock returns, especially focusing on the tail-side properties. we also propose a two-step iterative algorithm to train the model and then predict the time-varying model parameters, including the time-invariant tail parameters. at each investment date, we can easily simulate new samples from the learned generative model, and we further perform cvar portfolio optimization with the simulated samples to form a dynamic portfolio strategy. the numerical experiment on stock data shows that our model leads to wiser investments that promise higher reward-risk ratios and present lower tail risks.",
"categories": "q-fin.pm",
"doi": "",
"created": "2023-01-18",
"updated": "2024-01-16",
"authors": [
"chuting sun",
"qi wu",
"xing yan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2301.07318"
} | "2024-03-15T06:00:53.804038" | {
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} | [] | "algorithm" | "35dbd100-908a-49a6-a53b-82b8ac388509" | 1979 | hard |
|
\begin{algorithm}[t]
\begin{algorithmic}
\State \textbf{Input:} Independent initial samples $x_1^{(0)},...,x_N^{(0)}$ from $\mu_0$, momentum parameters $m_l\in[0,1)$ for $l=1,...,L$.
\State Initialize $(v_1,...,v_N)=0$.
\For{$l=1,...,L$}
\State - Set $(\tilde x_1^{(0)},...,\tilde x_N^{(0)})=(x_1^{(l-1)},...,x_N^{(l-1)})$.
\State - Simulate $T_l$ steps of the (momentum) MMD flow:
\For{$t=1,...,T_l$}
\State - Update $v$ by
\begin{align*}
(v_1,...,v_N)\leftarrow \nabla F_d(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)}|y_1,...,y_M)+m_l (v_1,...,v_N)
\end{align*}
\State - Update the flow samples:
\begin{align*}
(\tilde x_1^{(t)},...,\tilde x_N^{(t)})=(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)})-\tau N\ (v_1,...,v_N)
\end{align*}
\EndFor
\State - Train $\Phi_l$ such that $\tilde x^{(T_l)}\approx \tilde x_i^{(0)}-\Phi_l(\tilde x_i^{(0)}) $ by minimizing the loss
\begin{align*}
\mathcal L(\theta_l)=\frac1N\sum_{i=1}^N \|\Phi_l(\tilde x_i^{(0)})-(\tilde x_i^{(0)}-\tilde x_i^{(T_l)})\|^2.
\end{align*}
\State - Set $(x_1^{(l)},...,x_N^{(l)})=(x_1^{(l-1)},...,x_N^{(l-1)})-(\Phi_l(x_1^{(l-1)}),...,\Phi_l(x_N^{(l-1)}))$.
\EndFor
\end{algorithmic}
\caption{Training of generative MMD flows}
\label{alg:training_gen_MMD_flows}
\end{algorithm}
| \begin{algorithm}
[t]
\begin{algorithmic}
\State \textbf{Input:} Independent initial samples $x_1^{(0)},...,x_N^{(0)}$ from $\mu_0$, momentum parameters $m_l\in[0,1)$ for $l=1,...,L$.
\State Initialize $(v_1,...,v_N)=0$.
\For{$l=1,...,L$}
\State - Set $(\tilde x_1^{(0)},...,\tilde x_N^{(0)})=(x_1^{(l-1)},...,x_N^{(l-1)})$.
\State - Simulate $T_l$ steps of the (momentum) MMD flow:
\For{$t=1,...,T_l$}
\State - Update $v$ by
\begin{align*}
(v_1,...,v_N)\leftarrow \nabla F_d(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)}|y_1,...,y_M)+m_l (v_1,...,v_N)
\end{align*}
\State - Update the flow samples:
\begin{align*}
(\tilde x_1^{(t)},...,\tilde x_N^{(t)})=(\tilde x_1^{(t-1)},...,\tilde x_N^{(t-1)})-\tau N\ (v_1,...,v_N)
\end{align*}
\EndFor
\State - Train $\Phi_l$ such that $\tilde x^{(T_l)}\approx \tilde x_i^{(0)}-\Phi_l(\tilde x_i^{(0)}) $ by minimizing the loss
\begin{align*}
\mathcal L(\theta_l)=\frac1N\sum_{i=1}^N \|\Phi_l(\tilde x_i^{(0)})-(\tilde x_i^{(0)}-\tilde x_i^{(T_l)})\|^2.
\end{align*}
\State - Set $(x_1^{(l)},...,x_N^{(l)})=(x_1^{(l-1)},...,x_N^{(l-1)})-(\Phi_l(x_1^{(l-1)}),...,\Phi_l(x_N^{(l-1)}))$.
\EndFor
\end{algorithmic}
\caption{Training of generative MMD flows}
\end{algorithm} | "https://arxiv.org/src/2305.11463" | "2305.11463.tar.gz" | "2024-02-20" | {
"title": "generative sliced mmd flows with riesz kernels",
"id": "2305.11463",
"abstract": "maximum mean discrepancy (mmd) flows suffer from high computational costs in large scale computations. in this paper, we show that mmd flows with riesz kernels $k(x,y) = - \\|x-y\\|^r$, $r \\in (0,2)$ have exceptional properties which allow their efficient computation. we prove that the mmd of riesz kernels, which is also known as energy distance, coincides with the mmd of their sliced version. as a consequence, the computation of gradients of mmds can be performed in the one-dimensional setting. here, for $r=1$, a simple sorting algorithm can be applied to reduce the complexity from $o(mn+n^2)$ to $o((m+n)\\log(m+n))$ for two measures with $m$ and $n$ support points. as another interesting follow-up result, the mmd of compactly supported measures can be estimated from above and below by the wasserstein-1 distance. for the implementations we approximate the gradient of the sliced mmd by using only a finite number $p$ of slices. we show that the resulting error has complexity $o(\\sqrt{d/p})$, where $d$ is the data dimension. these results enable us to train generative models by approximating mmd gradient flows by neural networks even for image applications. we demonstrate the efficiency of our model by image generation on mnist, fashionmnist and cifar10.",
"categories": "cs.lg math.pr stat.ml",
"doi": "",
"created": "2023-05-19",
"updated": "2024-02-20",
"authors": [
"johannes hertrich",
"christian wald",
"fabian altekr\u00fcger",
"paul hagemann"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2305.11463"
} | "2024-03-15T04:32:53.456595" | {
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} | [] | "algorithm" | "80f4ac37-c1ba-4f04-8d61-69501d168731" | 1205 | hard |
|
\begin{algorithmic}
\For{\texttt{k in} $1:5000$}
\State \text{Draw from joint prior: } $\boldsymbol{\theta}^{sim}_k \sim\pi (\boldsymbol{\theta})$
\State \text{Simulate data set with 1000 observations: } $\boldsymbol{y}^{sim}_k \sim \pi(\boldsymbol{y}|\boldsymbol{\theta}^{sim}_k)$
\State \text{Draw 999 posterior samples post burn in:} $\{\boldsymbol{\theta}_1,\dots , \boldsymbol{\theta}_{999}\}_k \sim \pi(\boldsymbol{\theta} | \boldsymbol{y}^{sim}_k)$
\State \text{Compute rank statistics:} $\boldsymbol{r} = \mathrm{rank}(\{\boldsymbol{\theta}_1,\dots , \boldsymbol{\theta}_{999}\}_k, \boldsymbol{\theta}^{sim}_k)$
\EndFor
\end{algorithmic}
| \begin{algorithmic}
\For{\texttt{k in} $1:5000$}
\State \text{Draw from joint prior: } $\boldsymbol{\theta}^{sim}_k \sim\pi (\boldsymbol{\theta})$
\State \text{Simulate data set with 1000 observations: } $\boldsymbol{y}^{sim}_k \sim \pi(\boldsymbol{y}|\boldsymbol{\theta}^{sim}_k)$
\State \text{Draw 999 posterior samples post burn in:} $\{\boldsymbol{\theta}_1,\dots , \boldsymbol{\theta}_{999}\}_k \sim \pi(\boldsymbol{\theta} | \boldsymbol{y}^{sim}_k)$
\State \text{Compute rank statistics:} $\boldsymbol{r} = \mathrm{rank}(\{\boldsymbol{\theta}_1,\dots , \boldsymbol{\theta}_{999}\}_k, \boldsymbol{\theta}^{sim}_k)$
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2402.12384" | "2402.12384.tar.gz" | "2024-01-27" | {
"title": "comparing mcmc algorithms in stochastic volatility models using simulation based calibration",
"id": "2402.12384",
"abstract": "simulation based calibration (sbc) is applied to analyse two commonly used, competing markov chain monte carlo algorithms for estimating the posterior distribution of a stochastic volatility model. in particular, the bespoke 'off-set mixture approximation' algorithm proposed by kim, shephard, and chib (1998) is explored together with a hamiltonian monte carlo algorithm implemented through stan. the sbc analysis involves a simulation study to assess whether each sampling algorithm has the capacity to produce valid inference for the correctly specified model, while also characterising statistical efficiency through the effective sample size. results show that stan's no-u-turn sampler, an implementation of hamiltonian monte carlo, produces a well-calibrated posterior estimate while the celebrated off-set mixture approach is less efficient and poorly calibrated, though model parameterisation also plays a role. limitations and restrictions of generality are discussed.",
"categories": "stat.ap econ.em",
"doi": "",
"created": "2024-01-27",
"updated": "",
"authors": [
"benjamin wee"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.12384"
} | "2024-03-15T03:27:09.183136" | {
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} | [] | "algorithm" | "bdeae886-45cf-4bc7-8de5-6c53fb4b2f0e" | 645 | easy |
|
\begin{algorithmic}[1]
\State Initialise $(w_1^k)_0=(w_2^k)_0=,...,(w_M^k)_0=\frac{1}{M}$
\State $i \gets 0$
\State $\overline{\text{LogS}}_0^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_0 \cdot \hat{f}_m(y_{i,j}))$
\While{$i < \text{MaxIters}$}
\State Calculate the Log Score: $\overline{\text{LogS}}_i^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i} \cdot \hat{f}_m(y_{i,j}))$
\State Update the combination weights: $(w_m^k)_{i+1} = (w_m^k)_{i}\sum_{y_{ij} \in D_{val}^{k*}}\frac{\hat{f}_m(y_{i,j})}{\sum_{l=1}^{M}\hat{f}_l(y_{i,j})(w_l^k)_{i}}$
\State Update the Log Score: $\overline{\text{LogS}}_{i+1}^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i+1} \cdot \hat{f}_m(y_{i,j}))$
\If{$\overline{\text{LogS}}_{i+1}^k-\overline{\text{LogS}}_{i}^k < 10^{-16}$}
\State break
\EndIf
\State $i=i+1$
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Initialise $(w_1^k)_0=(w_2^k)_0=,...,(w_M^k)_0=\frac{1}{M}$
\State $i \gets 0$
\State $\overline{\text{LogS}}_0^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_0 \cdot \hat{f}_m(y_{i,j}))$
\While{$i < \text{MaxIters}$}
\State Calculate the Log Score: $\overline{\text{LogS}}_i^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i} \cdot \hat{f}_m(y_{i,j}))$
\State Update the combination weights: $(w_m^k)_{i+1} = (w_m^k)_{i}\sum_{y_{ij} \in D_{val}^{k*}}\frac{\hat{f}_m(y_{i,j})}{\sum_{l=1}^{M}\hat{f}_l(y_{i,j})(w_l^k)_{i}}$
\State Update the Log Score: $\overline{\text{LogS}}_{i+1}^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i+1} \cdot \hat{f}_m(y_{i,j}))$
\If{$\overline{\text{LogS}}_{i+1}^k-\overline{\text{LogS}}_{i}^k < 10^{-16}$}
\State break
\EndIf
\State $i=i+1$
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2206.08541" | "2206.08541.tar.gz" | "2024-02-19" | {
"title": "ensemble distributional forecasting for insurance loss reserving",
"id": "2206.08541",
"abstract": "loss reserving generally focuses on identifying a single model that can generate superior predictive performance. however, different loss reserving models specialise in capturing different aspects of loss data. this is recognised in practice in the sense that results from different models are often considered, and sometimes combined. for instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. in this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple _stochastic_ loss reserving models such that the strengths offered by different models can be utilised effectively. our framework contains two main innovations compared to existing literature and practice. firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. secondly, our framework is that it is tailored for the features inherent to reserving data. these include, for instance, accident, development, calendar, and claim maturity effects. crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. our framework is illustrated with a complex synthetic dataset. in the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. in particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators).",
"categories": "stat.me q-fin.rm stat.ap",
"doi": "",
"created": "2022-06-17",
"updated": "2024-02-19",
"authors": [
"benjamin avanzi",
"yanfeng li",
"bernard wong",
"alan xian"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.08541"
} | "2024-03-15T04:26:48.962440" | {
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} | [] | "algorithm" | "ab3164e2-32b4-46f8-9f03-873eaaa5ab4c" | 962 | medium |
|
\begin{algorithmic}[1]
\Require trajectory $\tau$
\For{layer $i$ in HKSL (begin with the lowest layer)}
\For{layer $j$ in HKSL (begin with the highest layer)}
\If{$i == j$}
\State break loop
\EndIf
\State Embed first observation $o$ in $\tau$ using layer $j$'s encoder
\If{layer $j$ is the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model and actions from $\tau$
\State Store the prediction
\EndFor
\Else{ layer $j$ is not the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Store the prediction
\EndFor
\EndIf
\EndFor
\State Embed first observation $o$ in $\tau$ using layer $i$'s encoder
\For{step layer $i$ can take in $\tau$}
\State Compute forward-step using layer $i$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Project the forward model's output with layer $i$'s nonlinear projection
\State Compute loss per Equation~\ref{eqn:hksl-loss}
\EndFor
\State Update layer $i$'s weights
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require trajectory $\tau$
\For{layer $i$ in HKSL (begin with the lowest layer)}
\For{layer $j$ in HKSL (begin with the highest layer)}
\If{$i == j$}
\State break loop
\EndIf
\State Embed first observation $o$ in $\tau$ using layer $j$'s encoder
\If{layer $j$ is the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model and actions from $\tau$
\State Store the prediction
\EndFor
\Else{ layer $j$ is not the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Store the prediction
\EndFor
\EndIf
\EndFor
\State Embed first observation $o$ in $\tau$ using layer $i$'s encoder
\For{step layer $i$ can take in $\tau$}
\State Compute forward-step using layer $i$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Project the forward model's output with layer $i$'s nonlinear projection
\State Compute loss per Equation~\ref{eqn:hksl-loss}
\EndFor
\State Update layer $i$'s weights
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2206.11396" | "2206.11396.tar.gz" | "2024-01-29" | {
"title": "multi-horizon representations with hierarchical forward models for reinforcement learning",
"id": "2206.11396",
"abstract": "learning control from pixels is difficult for reinforcement learning (rl) agents because representation learning and policy learning are intertwined. previous approaches remedy this issue with auxiliary representation learning tasks, but they either do not consider the temporal aspect of the problem or only consider single-step transitions, which may cause learning inefficiencies if important environmental changes take many steps to manifest. we propose hierarchical $k$-step latent (hksl), an auxiliary task that learns multiple representations via a hierarchy of forward models that learn to communicate and an ensemble of $n$-step critics that all operate at varying magnitudes of step skipping. we evaluate hksl in a suite of 30 robotic control tasks with and without distractors and a task of our creation. we find that hksl either converges to higher or optimal episodic returns more quickly than several alternative representation learning approaches. furthermore, we find that hksl's representations capture task-relevant details accurately across timescales (even in the presence of distractors) and that communication channels between hierarchy levels organize information based on both sides of the communication process, both of which improve sample efficiency.",
"categories": "cs.lg",
"doi": "",
"created": "2022-06-22",
"updated": "2024-01-29",
"authors": [
"trevor mcinroe",
"lukas sch\u00e4fer",
"stefano v. albrecht"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.11396"
} | "2024-03-15T08:37:32.877079" | {
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} | [] | "algorithm" | "49b1c20c-7c84-4acf-bc3b-44875eb26979" | 1227 | hard |
|
\begin{algorithmic}[1]
\Require $A$, $b$, $x_{0}=\mathbf{0}$
\For{$k=1,2,\ldots,$}
\State Compute $p_k$, $q_k$, $\alpha_k$, $\beta_k$ by the LBFRO \algorithmiccomment{roundoff unit is $\mathbf{u}$}
\State Compute $\rho_k$, $\theta_{k+1}$, $\bar{\rho}_{k+1}$, $\phi_{k}$, $\bar{\phi}_{k+1}$ by the updating procedure \algorithmiccomment{double precision}
\State Compute $x_k$, $w_{k+1}$ by the updating procedure \algorithmiccomment{roundoff unit is $\mathbf{\bar{u}}$}
\If{Early stopping criterion is satisfied} \algorithmiccomment{DP or L-curve criterion}
\State The semi-convergence point is estimated as $k_1$
\State Terminate the iteration
\EndIf
\EndFor
\Ensure Final regularized solution $\hat{x}_{k_1}$ \algorithmiccomment{Computed solution corresponding to $x_{k_1}$}
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require $A$, $b$, $x_{0}=\mathbf{0}$
\For{$k=1,2,\ldots,$}
\State Compute $p_k$, $q_k$, $\alpha_k$, $\beta_k$ by the LBFRO \algorithmiccomment{roundoff unit is $\mathbf{u}$}
\State Compute $\rho_k$, $\theta_{k+1}$, $\bar{\rho}_{k+1}$, $\phi_{k}$, $\bar{\phi}_{k+1}$ by the updating procedure \algorithmiccomment{double precision}
\State Compute $x_k$, $w_{k+1}$ by the updating procedure \algorithmiccomment{roundoff unit is $\mathbf{\bar{u}}$}
\If{Early stopping criterion is satisfied} \algorithmiccomment{DP or L-curve criterion}
\State The semi-convergence point is estimated as $k_1$
\State Terminate the iteration
\EndIf
\EndFor
\Ensure Final regularized solution $\hat{x}_{k_1}$ \algorithmiccomment{Computed solution corresponding to $x_{k_1}$}
\end{algorithmic} | "https://arxiv.org/src/2210.11025" | "2210.11025.tar.gz" | "2024-02-12" | {
"title": "double precision is not necessary for lsqr for solving discrete linear ill-posed problems",
"id": "2210.11025",
"abstract": "the growing availability and usage of low precision foating point formats has attracts many interests of developing lower or mixed precision algorithms for scientific computing problems. in this paper we investigate the possibility of exploiting lower precision computing in lsqr for solving discrete linear ill-posed problems. we analyze the choice of proper computing precisions in the two main parts of lsqr, including the construction of lanczos vectors and updating procedure of iterative solutions. we show that, under some mild conditions, the lanczos vectors can be computed using single precision without loss of any accuracy of final regularized solutions as long as the noise level is not extremely small. we also show that the most time consuming part for updating iterative solutions can be performed using single precision without sacrificing any accuracy. the results indicate that the most time consuming parts of the algorithm can be implemented using single precision, and thus the performance of lsqr for solving discrete linear ill-posed problems can be significantly enhanced. numerical experiments are made for testing the single precision variants of lsqr and confirming our results.",
"categories": "math.na cs.na",
"doi": "10.1007/s10915-023-02447-4",
"created": "2022-10-20",
"updated": "2024-02-12",
"authors": [
"haibo li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.11025"
} | "2024-03-15T04:23:06.439214" | {
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} | [] | "algorithm" | "361d2e88-f516-4671-b1a7-cdde90b03105" | 794 | medium |
|
\begin{algorithm}
\caption{Compute $c^*$}\label{alg:find_cstar}
\begin{algorithmic}
\Require $a_i, B_i, \theta_i$
\\
\State Sort the values $a_i, \theta_i$ according to $\frac{a_{ij}}{\theta_{ij}}$ in a descending order.
If there are goods with $\theta_{ij} = 0$, sort them separately according to $a_{ij}$ and place them as a prefix (lower indices) before the other sorted goods. Equal values are sorted in a lexicographical order.
\\
\State Set: $a \gets 0,\quad \theta \gets 0,\quad c_s\gets 0,\quad c^* \gets 0$
\For{$j = 1, \dots, m$}
\State $a \gets a + a_{ij},\ \theta \gets \theta + \theta_{ij}$
\State $c_s \gets \frac{a}{\theta + B_i}$
\State $c^* \gets \max\{c^*, c_s\}$
\EndFor
\State \Return $c^*$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Compute $c^*$}\begin{algorithmic}
\Require $a_i, B_i, \theta_i$
\\
\State Sort the values $a_i, \theta_i$ according to $\frac{a_{ij}}{\theta_{ij}}$ in a descending order.
If there are goods with $\theta_{ij} = 0$, sort them separately according to $a_{ij}$ and place them as a prefix (lower indices) before the other sorted goods. Equal values are sorted in a lexicographical order.
\\
\State Set: $a \gets 0,\quad \theta \gets 0,\quad c_s\gets 0,\quad c^* \gets 0$
\For{$j = 1, \dots, m$}
\State $a \gets a + a_{ij},\ \theta \gets \theta + \theta_{ij}$
\State $c_s \gets \frac{a}{\theta + B_i}$
\State $c^* \gets \max\{c^*, c_s\}$
\EndFor
\State \Return $c^*$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2307.04108" | "2307.04108.tar.gz" | "2024-01-15" | {
"title": "asynchronous proportional response dynamics in markets with adversarial scheduling",
"id": "2307.04108",
"abstract": "we study proportional response dynamics (prd) in linear fisher markets where participants act asynchronously. we model this scenario as a sequential process in which in every step, an adversary selects a subset of the players that will update their bids, subject to liveness constraints. we show that if every bidder individually uses the prd update rule whenever they are included in the group of bidders selected by the adversary, then (in the generic case) the entire dynamic converges to a competitive equilibrium of the market. our proof technique uncovers further properties of linear fisher markets, such as the uniqueness of the equilibrium for generic parameters and the convergence of associated best-response dynamics and no-swap regret dynamics under certain conditions.",
"categories": "cs.gt cs.ma econ.th math.ds",
"doi": "",
"created": "2023-07-09",
"updated": "2024-01-15",
"authors": [
"yoav kolumbus",
"menahem levy",
"noam nisan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2307.04108"
} | "2024-03-15T06:09:48.864469" | {
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} | [] | "algorithm" | "0bacbbc9-4d09-4d9e-94ec-d435646ac257" | 721 | medium |
|
\begin{algorithm}\label{alg: tau-best}
\begin{enumerate}
\item Set $J_0=J$ and $I=J^{\rm lower}$.
\item Perform Steps 3--5 of Algorithm~\ref{alg:marg sim CS} to obtain $R_n\equiv \prod_{j\in J_0} R_{n,j}$.
\item Construct $R^{\tau-\rm{best}}_n$ as defined in \eqref{eq: def proj tau-best}.
\end{enumerate}
\end{algorithm}
| \begin{algorithm}
\begin{enumerate}
\item Set $J_0=J$ and $I=J^{\rm lower}$.
\item Perform Steps 3--5 of Algorithm~\ref{alg:marg sim CS} to obtain $R_n\equiv \prod_{j\in J_0} R_{n,j}$.
\item Construct $R^{\tau-\rm{best}}_n$ as defined in \eqref{eq: def proj tau-best}.
\end{enumerate}
\end{algorithm} | "https://arxiv.org/src/2402.00192" | "2402.00192.tar.gz" | "2024-01-31" | {
"title": "finite- and large-sample inference for ranks using multinomial data with an application to ranking political parties",
"id": "2402.00192",
"abstract": "it is common to rank different categories by means of preferences that are revealed through data on choices. a prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. in this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. we consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. a distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. we additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. we use our methodology to rank political parties in australia using data from the 2019 australian election survey. we find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. in contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. these findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.",
"categories": "econ.em",
"doi": "",
"created": "2024-01-31",
"updated": "",
"authors": [
"sergei bazylik",
"magne mogstad",
"joseph romano",
"azeem shaikh",
"daniel wilhelm"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.00192"
} | "2024-03-15T05:13:20.067590" | {
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} | [] | "algorithm" | "ff73008d-5dfb-4af6-9bcc-04e80743973b" | 300 | easy |
|
\begin{algorithmic}[1]
\State Construct the IV $z_{t-1}$ by equation (\ref{mulivz}).
\State Construct the IV estimators $\hat{\beta}_{ivx}$, $\hat{\beta}_a$ and $\hat{\beta}_b$ using the full sample and two subsamples by equations (\ref{defdeftwo2}), (\ref{muldef2new}) and (\ref{muldef3new}).
\State Eliminate the DE: Construct the weighted IV estimator $\hat{\beta}_l \equiv (W_1-W_2-W_3)^{-1}(W_1 \hat{\beta}_{ivx}-W_2\hat{\beta}_a -W_3 \hat{\beta}_b)$, where $W_1=\sum\nolimits_{t=1}^{T} \bar{z}_{t-1} x_{t-1}^\top $, $W_2=S_a \sum\nolimits_{t=1}^{T_0} \left( z_{t-1}- \frac{1}{T_0}\sum\nolimits_{t=1}^{T_0} z_{t-1} \right) x_{t-1}^\top$ and
$W_3=S_b \sum\nolimits_{t=T_0+1}^{T} \left( z_{t-1}- \frac{1}{T-T_0}\sum\nolimits_{t=T_0+1}^{T} z_{t-1} \right) x_{t-1}^\top$.
\State Control size for both SD and WD predictors:
\begin{itemize}
\item Reduce the DiE: Construct the estimator $\hat{\beta}_m = \hat{\beta}_{l}+ {B_m} {W_z} T^{-(1 -\delta) / 2} \frac{K+1}{2}{\hat{\rho}_{u v^*}}/ \sqrt{-2 c_z}$, where
${B_m}\equiv \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left( \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}\left(\operatorname{I_K}+ {W_z}\hat{\varpi}_l\hat{\varpi}_l^\top{W_z}^\top \right)^{1/2}$.
\item Reduce the VEE: Construct the estimator for the asymptotic covariance matrix of as $\operatorname{\widehat{Avar}}(\hat{\beta}_m ) \equiv H_l \left(\operatorname{I_K}+{W_z}\hat{\varpi}_l\hat{\varpi}_l^\top {W_z}^\top \right) H_l^\top$, where
$
H_l = \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left(\frac{T}{T-2K-1} \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}
$.
\item \textcolor{black}{Reduce the size distortion induced by the variance of the estimator of $u_t$: Use Lagrange-multiplier principle to obtain $\hat{u}_t= y_t - \hat{\mu}_s - x_{t-1}^\top \hat{\beta}_s$ by the constrained OLS estimation
$(\hat{\mu}_s,\hat{\beta}_s)^\top = \arg\, \min_{\mu,\beta} \left( y_t - \mu - x_{t-1}^\top \beta\right)^2,
\ s.t. \quad R\beta =r_J$.}
\end{itemize}
\State Construct the test statistic ${Q_m} \equiv \left(R \hat{\beta}_m -r_J \right)^\top \left[R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{-1} \left(R \hat{\beta}_m -r_J \right)$ with SD and WD predictors for $H_0:R\beta =r_J$.
\If{Focus on the one-sided marginal test $H_0:\beta_i=0$ vs $H_a:\beta_i>0$ and $H_0:\beta_i=0$ vs $H_a:\beta_i<0$ }
\State Construct the t-test statistic ${Q_m^t} \equiv \frac{R \hat{\beta}_m -r_J}{ \left[ R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{1/2}}$.
\EndIf
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Construct the IV $z_{t-1}$ by equation (\ref{mulivz}).
\State Construct the IV estimators $\hat{\beta}_{ivx}$, $\hat{\beta}_a$ and $\hat{\beta}_b$ using the full sample and two subsamples by equations (\ref{defdeftwo2}), (\ref{muldef2new}) and (\ref{muldef3new}).
\State Eliminate the DE: Construct the weighted IV estimator $\hat{\beta}_l \equiv (W_1-W_2-W_3)^{-1}(W_1 \hat{\beta}_{ivx}-W_2\hat{\beta}_a -W_3 \hat{\beta}_b)$, where $W_1=\sum\nolimits_{t=1}^{T} \bar{z}_{t-1} x_{t-1}^\top $, $W_2=S_a \sum\nolimits_{t=1}^{T_0} \left( z_{t-1}- \frac{1}{T_0}\sum\nolimits_{t=1}^{T_0} z_{t-1} \right) x_{t-1}^\top$ and
$W_3=S_b \sum\nolimits_{t=T_0+1}^{T} \left( z_{t-1}- \frac{1}{T-T_0}\sum\nolimits_{t=T_0+1}^{T} z_{t-1} \right) x_{t-1}^\top$.
\State Control size for both SD and WD predictors:
\begin{itemize}
\item Reduce the DiE: Construct the estimator $\hat{\beta}_m = \hat{\beta}_{l}+ {B_m} {W_z} T^{-(1 -\delta) / 2} \frac{K+1}{2}{\hat{\rho}_{u v^*}}/ \sqrt{-2 c_z}$, where
${B_m}\equiv \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left( \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}\left(\operatorname{I_K}+ {W_z}\hat{\varpi}_l\hat{\varpi}_l^\top{W_z}^\top \right)^{1/2}$.
\item Reduce the VEE: Construct the estimator for the asymptotic covariance matrix of as $\operatorname{\widehat{Avar}}(\hat{\beta}_m ) \equiv H_l \left(\operatorname{I_K}+{W_z}\hat{\varpi}_l\hat{\varpi}_l^\top {W_z}^\top \right) H_l^\top$, where
$
H_l = \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left(\frac{T}{T-2K-1} \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}
$.
\item \textcolor{black}{Reduce the size distortion induced by the variance of the estimator of $u_t$: Use Lagrange-multiplier principle to obtain $\hat{u}_t= y_t - \hat{\mu}_s - x_{t-1}^\top \hat{\beta}_s$ by the constrained OLS estimation
$(\hat{\mu}_s,\hat{\beta}_s)^\top = \arg\, \min_{\mu,\beta} \left( y_t - \mu - x_{t-1}^\top \beta\right)^2,
\ s.t. \quad R\beta =r_J$.}
\end{itemize}
\State Construct the test statistic ${Q_m} \equiv \left(R \hat{\beta}_m -r_J \right)^\top \left[R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{-1} \left(R \hat{\beta}_m -r_J \right)$ with SD and WD predictors for $H_0:R\beta =r_J$.
\If{Focus on the one-sided marginal test $H_0:\beta_i=0$ vs $H_a:\beta_i>0$ and $H_0:\beta_i=0$ vs $H_a:\beta_i<0$ }
\State Construct the t-test statistic ${Q_m^t} \equiv \frac{R \hat{\beta}_m -r_J}{ \left[ R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{1/2}}$.
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2401.01064" | "2401.01064.tar.gz" | "2024-01-02" | {
"title": "robust inference for multiple predictive regressions with an application on bond risk premia",
"id": "2401.01064",
"abstract": "we propose a robust hypothesis testing procedure for the predictability of multiple predictors that could be highly persistent. our method improves the popular extended instrumental variable (ivx) testing (phillips and lee, 2013; kostakis et al., 2015) in that, besides addressing the two bias effects found in hosseinkouchack and demetrescu (2021), we find and deal with the variance-enlargement effect. we show that two types of higher-order terms induce these distortion effects in the test statistic, leading to significant over-rejection for one-sided tests and tests in multiple predictive regressions. our improved ivx-based test includes three steps to tackle all the issues above regarding finite sample bias and variance terms. thus, the test statistics perform well in size control, while its power performance is comparable with the original ivx. monte carlo simulations and an empirical study on the predictability of bond risk premia are provided to demonstrate the effectiveness of the newly proposed approach.",
"categories": "stat.me econ.em",
"doi": "",
"created": "2024-01-02",
"updated": "",
"authors": [
"xiaosai liao",
"xinjue li",
"qingliang fan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.01064"
} | "2024-03-15T06:49:14.014471" | {
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} | [] | "algorithm" | "f1710741-93ba-4b6e-9b20-3a516fbf4d3b" | 2612 | hard |
|
\begin{algorithmic}[1]
\item \textbf{Input:} $X = \langle X_{(t-T+1)}, X_{(t-T+2)}, \ldots, X_{t}\rangle; \quad X \in \mathbb{R}^{N \times T \times 1}$
\item \textbf{Output:} $ \widetilde{Y} = \langle X_{(t+1)}, X_{(t+2)}, \ldots, X_{\left(t+T^{\prime}\right)}\rangle; \quad \widetilde{Y} \in \mathbb{R}^{N \times T \times 1}$
\item \textbf{Parameters:} \texttt{Randomly initialize $\Theta$ and hidden state $H_{t-1}$}
\For{\texttt{all} $T$}
\State $X_{t^{\prime}} \gets X[:,t,:]; \quad X_{t^{\prime}} \in \mathbb{R}^{N \times 1} $
\State $X_t=\xi_{\theta}\left(X_{t^{\prime}}\right) ; \quad X_t\in R^{N \times C^{\prime}}$ \Comment{followed by eq. ~\ref{eqn:eqn2}}
\State $H_{t-1} = {STLGRU}_{\Theta} \left( X_t,H_{t-1} \right)$
\EndFor
\State $H_t= H_{t-1}$
\State $\hat{Y} = OutputLayer(H_t)$ \Comment{followed by eq. ~\ref{function}}
\State calculate loss $L$ using eq. ~\ref{final}
\State \textbf{return} $\hat{Y} $
\end{algorithmic}
| \begin{algorithmic}
[1]
\item \textbf{Input:} $X = \langle X_{(t-T+1)}, X_{(t-T+2)}, \ldots, X_{t}\rangle; \quad X \in \mathbb{R}^{N \times T \times 1}$
\item \textbf{Output:} $ \widetilde{Y} = \langle X_{(t+1)}, X_{(t+2)}, \ldots, X_{\left(t+T^{\prime}\right)}\rangle; \quad \widetilde{Y} \in \mathbb{R}^{N \times T \times 1}$
\item \textbf{Parameters:} \texttt{Randomly initialize $\Theta$ and hidden state $H_{t-1}$}
\For{\texttt{all} $T$}
\State $X_{t^{\prime}} \gets X[:,t,:]; \quad X_{t^{\prime}} \in \mathbb{R}^{N \times 1} $
\State $X_t=\xi_{\theta}\left(X_{t^{\prime}}\right) ; \quad X_t\in R^{N \times C^{\prime}}$ \Comment{followed by eq. ~\ref{eqn:eqn2}}
\State $H_{t-1} = {STLGRU}_{\Theta} \left( X_t,H_{t-1} \right)$
\EndFor
\State $H_t= H_{t-1}$
\State $\hat{Y} = OutputLayer(H_t)$ \Comment{followed by eq. ~\ref{function}}
\State calculate loss $L$ using eq. ~\ref{final}
\State \textbf{return} $\hat{Y} $
\end{algorithmic} | "https://arxiv.org/src/2212.04548" | "2212.04548.tar.gz" | "2024-02-19" | {
"title": "stlgru: spatio-temporal lightweight graph gru for traffic flow prediction",
"id": "2212.04548",
"abstract": "reliable forecasting of traffic flow requires efficient modeling of traffic data. indeed, different correlations and influences arise in a dynamic traffic network, making modeling a complicated task. existing literature has proposed many different methods to capture traffic networks' complex underlying spatial-temporal relations. however, given the heterogeneity of traffic data, consistently capturing both spatial and temporal dependencies presents a significant challenge. also, as more and more sophisticated methods are being proposed, models are increasingly becoming memory-heavy and, thus, unsuitable for low-powered devices. to this end, we propose spatio-temporal lightweight graph gru, namely stlgru, a novel traffic forecasting model for predicting traffic flow accurately. specifically, our proposed stlgru can effectively capture dynamic local and global spatial-temporal relations of traffic networks using memory-augmented attention and gating mechanisms in a continuously synchronized manner. moreover, instead of employing separate temporal and spatial components, we show that our memory module and gated unit can successfully learn the spatial-temporal dependencies with reduced memory usage and fewer parameters. extensive experimental results on three real-world public traffic datasets demonstrate that our method can not only achieve state-of-the-art performance but also exhibit competitive computational efficiency. our code is available at https://github.com/kishor-bhaumik/stlgru",
"categories": "cs.lg",
"doi": "",
"created": "2022-12-08",
"updated": "2024-02-19",
"authors": [
"kishor kumar bhaumik",
"fahim faisal niloy",
"saif mahmud",
"simon woo"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.04548"
} | "2024-03-15T05:03:36.405412" | {
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} | [] | "algorithm" | "b3e95324-18ae-4fa8-ab16-f98f466463cd" | 939 | medium |
|
\begin{algorithmic}
\State \textbf{Input:} 1) fixed $L_s$; 2) current positions $X(t)$ of agents at time $t$; 3) a nondecreasing transition function $\xi:\mathbb{R}^+\to [0,1]$ (e.g. $\xi(s):=1-\sigma(s)$, see \textsection \ref{sec:weights})\\
\\
set $k=0$\\
set $Y=\emptyset$
\While{$true$}
\State for all $\mathbf{\mathbf{y}}\in \mathcal{S}_{r}$ let $R_\mathbf{y}:=\text{dist}(\mathbf{y};X\cup Y)$ and construct
\[
f_{k}(\mathbf{y}):=\begin{cases} \xi\left(R_\mathbf{y}\right/L_s-1) & \text{if }R_\mathbf{y}\geq L_{s}\\ 0 & \text{if }R_\mathbf{y}<L_{s}\\
\end{cases}
\]
\If{$f_k(\mathbf{y})\equiv 0$}
\State break (meaning $\mathcal{S}_{r}$ is saturated)
\EndIf
\State (a) normalize $f_{k}(\mathbf{y})$ so that $\int_{\mathcal{S}_{r}}f_{k}(\mathbf{y})d\mathbf{y}=1$
\State (b) generate the position $\mathbf{y}_k$ of the $k^{\text{th}}$ new agent
\State \quad on $\mathcal{S}_{r}$ by a random sampling using the PDF $f_k(y)$
\State (c) updates: $Y\leftarrow Y\cup \{\mathbf{y}_k\}$ and $k\leftarrow k+1$
\EndWhile
\State \textbf{Output:} $Y$ are the collected positions on $\mathcal{S}_{r}$ of the $k$ newly inserted agents to be added to $X(t)$.\\
\State \underline{NOTE}: it is possible that $k=0$ and $Y=\emptyset$, indicating that no new agent will enter at time $t$ due to $\mathcal{S}_{r}$ being overcrowded from the beginning.
\end{algorithmic}
| \begin{algorithmic}
\State \textbf{Input:} 1) fixed $L_s$; 2) current positions $X(t)$ of agents at time $t$; 3) a nondecreasing transition function $\xi:\mathbb{R}^+\to [0,1]$ (e.g. $\xi(s):=1-\sigma(s)$, see \textsection \ref{sec:weights})\\
\\
set $k=0$\\
set $Y=\emptyset$
\While{$true$}
\State for all $\mathbf{\mathbf{y}}\in \mathcal{S}_{r}$ let $R_\mathbf{y}:=\text{dist}(\mathbf{y};X\cup Y)$ and construct
\[
f_{k}(\mathbf{y}):=\begin{cases}
\xi\left(R_\mathbf{y}\right/L_s-1) & \text{if }R_\mathbf{y}\geq L_{s}\\ 0 & \text{if }R_\mathbf{y}<L_{s}\\
\end{cases}
\]
\If{$f_k(\mathbf{y})\equiv 0$}
\State break (meaning $\mathcal{S}_{r}$ is saturated)
\EndIf
\State (a) normalize $f_{k}(\mathbf{y})$ so that $\int_{\mathcal{S}_{r}}f_{k}(\mathbf{y})d\mathbf{y}=1$
\State (b) generate the position $\mathbf{y}_k$ of the $k^{\text{th}}$ new agent
\State \quad on $\mathcal{S}_{r}$ by a random sampling using the PDF $f_k(y)$
\State (c) updates: $Y\leftarrow Y\cup \{\mathbf{y}_k\}$ and $k\leftarrow k+1$
\EndWhile
\State \textbf{Output:} $Y$ are the collected positions on $\mathcal{S}_{r}$ of the $k$ newly inserted agents to be added to $X(t)$.\\
\State \underline{NOTE}: it is possible that $k=0$ and $Y=\emptyset$, indicating that no new agent will enter at time $t$ due to $\mathcal{S}_{r}$ being overcrowded from the beginning.
\end{algorithmic} | "https://arxiv.org/src/2111.03448" | "2111.03448.tar.gz" | "2024-02-13" | {
"title": "emergence of collective behaviors from local voronoi topological perception",
"id": "2111.03448",
"abstract": "this article addresses how diverse collective behaviors arise from simple and realistic decisions made entirely at the level of each agent's personal space in the sense of the voronoi diagram. we present a discrete time model in 2d in which individual agents are aware of their local voronoi environment and may seek static target locations. in particular, agents only communicate directly with their voronoi neighbors and make decisions based on the geometry of their own voronoi cells. with two effective control parameters, it is shown numerically to capture a wide range of collective behaviors in different scenarios. further, we show that the voronoi topology facilitates the computation of several novel observables for quantifying discrete collective behaviors. these observables are applicable to all agent-based models and to empirical data.",
"categories": "physics.soc-ph math.ds q-bio.pe",
"doi": "",
"created": "2021-10-29",
"updated": "2024-02-13",
"authors": [
"ivan gonzalez",
"jack tisdell",
"rustum choksi",
"jean-christophe nave"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2111.03448"
} | "2024-03-15T04:08:22.815847" | {
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} | [] | "algorithm" | "88895f2a-16d2-4871-8f56-b4703f063921" | 1353 | hard |
|
\begin{algorithm}[htb!]
Step 1: Initialize the parameters $\boldsymbol{\theta}$ of the neural
network $\hat{u}(\boldsymbol{x};\boldsymbol{\theta})$.\\
Step 2: Set up the training sets
$\left\{\boldsymbol{x}_{\Omega}\right\}$
and $\left\{\boldsymbol{x}_{\partial \Omega}\right\}$ for the equation
and
boundary/initial conditions, respectively.\\
Step 3: Define the loss function by calculating the weighted $L^2$
norm of
both the differential equation and boundary condition residuals.\\
Step 4: Train the neural network by minimizing the loss function
$\mathcal{L}(\boldsymbol{\theta})$ to obtain the optimal parameters
$\boldsymbol{\theta}^*$.
\caption{Physics-Informed Neural Network (PINN) algorithm for solving
differential equations.}
\label{algorithm:1}
\end{algorithm}
| \begin{algorithm}
[htb!]
Step 1: Initialize the parameters $\boldsymbol{\theta}$ of the neural
network $\hat{u}(\boldsymbol{x};\boldsymbol{\theta})$.\\
Step 2: Set up the training sets
$\left\{\boldsymbol{x}_{\Omega}\right\}$
and $\left\{\boldsymbol{x}_{\partial \Omega}\right\}$ for the equation
and
boundary/initial conditions, respectively.\\
Step 3: Define the loss function by calculating the weighted $L^2$
norm of
both the differential equation and boundary condition residuals.\\
Step 4: Train the neural network by minimizing the loss function
$\mathcal{L}(\boldsymbol{\theta})$ to obtain the optimal parameters
$\boldsymbol{\theta}^*$.
\caption{Physics-Informed Neural Network (PINN) algorithm for solving
differential equations.}
\end{algorithm} | "https://arxiv.org/src/2401.04378" | "2401.04378.tar.gz" | "2024-01-09" | {
"title": "computing the gerber-shiu function with interest and a constant dividend barrier by physics-informed neural networks",
"id": "2401.04378",
"abstract": "in this paper, we propose a new efficient method for calculating the gerber-shiu discounted penalty function. generally, the gerber-shiu function usually satisfies a class of integro-differential equation. we introduce the physics-informed neural networks (pinn) which embed a differential equation into the loss of the neural network using automatic differentiation. in addition, pinn is more free to set boundary conditions and does not rely on the determination of the initial value. this gives us an idea to calculate more general gerber-shiu functions. numerical examples are provided to illustrate the very good performance of our approximation.",
"categories": "math.na cs.na math.pr q-fin.rm",
"doi": "",
"created": "2024-01-09",
"updated": "",
"authors": [
"zan yu",
"lianzeng zhang"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.04378"
} | "2024-03-15T06:29:05.749339" | {
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} | [] | "algorithm" | "d155ec32-f60d-4e38-905f-74344f56ca57" | 756 | medium |
|
\begin{algorithm}[H]
\caption{Minorization-Maximisation algorithm for Log Score maximisation}\label{alg:algoMM}
\begin{algorithmic}[1]
\State Initialise $(w_1^k)_0=(w_2^k)_0=,...,(w_M^k)_0=\frac{1}{M}$
\State $i \gets 0$
\State $\overline{\text{LogS}}_0^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_0 \cdot \hat{f}_m(y_{i,j}))$
\While{$i < \text{MaxIters}$}
\State Calculate the Log Score: $\overline{\text{LogS}}_i^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i} \cdot \hat{f}_m(y_{i,j}))$
\State Update the combination weights: $(w_m^k)_{i+1} = (w_m^k)_{i}\sum_{y_{ij} \in D_{val}^{k*}}\frac{\hat{f}_m(y_{i,j})}{\sum_{l=1}^{M}\hat{f}_l(y_{i,j})(w_l^k)_{i}}$
\State Update the Log Score: $\overline{\text{LogS}}_{i+1}^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i+1} \cdot \hat{f}_m(y_{i,j}))$
\If{$\overline{\text{LogS}}_{i+1}^k-\overline{\text{LogS}}_{i}^k < 10^{-16}$}
\State break
\EndIf
\State $i=i+1$
\EndWhile
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Minorization-Maximisation algorithm for Log Score maximisation}\begin{algorithmic}
[1]
\State Initialise $(w_1^k)_0=(w_2^k)_0=,...,(w_M^k)_0=\frac{1}{M}$
\State $i \gets 0$
\State $\overline{\text{LogS}}_0^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_0 \cdot \hat{f}_m(y_{i,j}))$
\While{$i < \text{MaxIters}$}
\State Calculate the Log Score: $\overline{\text{LogS}}_i^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i} \cdot \hat{f}_m(y_{i,j}))$
\State Update the combination weights: $(w_m^k)_{i+1} = (w_m^k)_{i}\sum_{y_{ij} \in D_{val}^{k*}}\frac{\hat{f}_m(y_{i,j})}{\sum_{l=1}^{M}\hat{f}_l(y_{i,j})(w_l^k)_{i}}$
\State Update the Log Score: $\overline{\text{LogS}}_{i+1}^k \gets \frac{1}{|D_{val}^{k*}|} \sum_{y_{ij} \in D_{val}^{k*}} \ln (\sum_{m=1}^M (w_m^k)_{i+1} \cdot \hat{f}_m(y_{i,j}))$
\If{$\overline{\text{LogS}}_{i+1}^k-\overline{\text{LogS}}_{i}^k < 10^{-16}$}
\State break
\EndIf
\State $i=i+1$
\EndWhile
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2206.08541" | "2206.08541.tar.gz" | "2024-02-19" | {
"title": "ensemble distributional forecasting for insurance loss reserving",
"id": "2206.08541",
"abstract": "loss reserving generally focuses on identifying a single model that can generate superior predictive performance. however, different loss reserving models specialise in capturing different aspects of loss data. this is recognised in practice in the sense that results from different models are often considered, and sometimes combined. for instance, actuaries may take a weighted average of the prediction outcomes from various loss reserving models, often based on subjective assessments. in this paper, we propose a systematic framework to objectively combine (i.e. ensemble) multiple _stochastic_ loss reserving models such that the strengths offered by different models can be utilised effectively. our framework contains two main innovations compared to existing literature and practice. firstly, our criteria model combination considers the full distributional properties of the ensemble and not just the central estimate - which is of particular importance in the reserving context. secondly, our framework is that it is tailored for the features inherent to reserving data. these include, for instance, accident, development, calendar, and claim maturity effects. crucially, the relative importance and scarcity of data across accident periods renders the problem distinct from the traditional ensembling techniques in statistical learning. our framework is illustrated with a complex synthetic dataset. in the results, the optimised ensemble outperforms both (i) traditional model selection strategies, and (ii) an equally weighted ensemble. in particular, the improvement occurs not only with central estimates but also relevant quantiles, such as the 75th percentile of reserves (typically of interest to both insurers and regulators).",
"categories": "stat.me q-fin.rm stat.ap",
"doi": "",
"created": "2022-06-17",
"updated": "2024-02-19",
"authors": [
"benjamin avanzi",
"yanfeng li",
"bernard wong",
"alan xian"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.08541"
} | "2024-03-15T03:14:29.396980" | {
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} | [] | "algorithm" | "d4abd2a9-2115-43a4-8aaa-b5b870594c51" | 1072 | medium |
|
\begin{algorithmic}[1]
\State Select an initial estimate $\hat{\mathbf{c}}^{(1)}$, a maximum number of iterations $M_{\textnormal{iter}}$, and a tolerance factor $\epsilon$
\State $j\gets 1$, $\textnormal{flag}\gets 1$
\While{$j\leq M_{\textnormal{iter}}$ and $\textnormal{flag}=1$}
\State \textbf{E-step}: Compute the expectation
\begin{equation}
\label{qfunction}
Q(\mathbf{c},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.01cm}) \hspace{-0.04cm}= \hspace{-0.04cm}\mathbb{E}\hspace{-0.03cm}\left\{ \log \textnormal{p}(\mathbf{z}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\mathcal{Y}_{1:N}|\mathbf{c}\hspace{-0.02cm})|\mathcal{Y}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.04cm}\right\}\hspace{-0.03cm}.\hspace{-0.1cm}
\end{equation}
\State \textbf{M-step}: Solve the optimization problem
\begin{equation}
\label{mstep}
\hat{\mathbf{c}}^{(j+1)} = \underset{\mathbf{c}\in \mathbb{R}^N}{\arg \max} \left( Q(\mathbf{c},\hat{\mathbf{c}}^{(j)}) -\frac{\gamma\mathbf{c}^{\top}\mathbf{Kc}}{2} \right).
\end{equation}
\If{$\dfrac{\|\hat{\mathbf{c}}^{(j+1)}-\hat{\mathbf{c}}^{(j)}\|_2}{\|\hat{\mathbf{c}}^{(j)}\|_2}<\epsilon$} \State $\textnormal{flag} \gets 0$
\EndIf
\State $j \gets j+1$
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Select an initial estimate $\hat{\mathbf{c}}^{(1)}$, a maximum number of iterations $M_{\textnormal{iter}}$, and a tolerance factor $\epsilon$
\State $j\gets 1$, $\textnormal{flag}\gets 1$
\While{$j\leq M_{\textnormal{iter}}$ and $\textnormal{flag}=1$}
\State \textbf{E-step}: Compute the expectation
\begin{equation*}
Q(\mathbf{c},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.01cm}) \hspace{-0.04cm}= \hspace{-0.04cm}\mathbb{E}\hspace{-0.03cm}\left\{ \log \textnormal{p}(\mathbf{z}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\mathcal{Y}_{1:N}|\mathbf{c}\hspace{-0.02cm})|\mathcal{Y}_{1:N}\hspace{-0.02cm},\hspace{-0.02cm}\hat{\mathbf{c}}^{(j)}\hspace{-0.04cm}\right\}\hspace{-0.03cm}.\hspace{-0.1cm}
\end{equation*}
\State \textbf{M-step}: Solve the optimization problem
\begin{equation*}
\hat{\mathbf{c}}^{(j+1)} = \underset{\mathbf{c}\in \mathbb{R}^N}{\arg \max} \left( Q(\mathbf{c},\hat{\mathbf{c}}^{(j)}) -\frac{\gamma\mathbf{c}^{\top}\mathbf{Kc}}{2} \right).
\end{equation*}
\If{$\dfrac{\|\hat{\mathbf{c}}^{(j+1)}-\hat{\mathbf{c}}^{(j)}\|_2}{\|\hat{\mathbf{c}}^{(j)}\|_2}<\epsilon$} \State $\textnormal{flag} \gets 0$
\EndIf
\State $j \gets j+1$
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2303.06045" | "2303.06045.tar.gz" | "2024-02-23" | {
"title": "kernel-based identification using lebesgue-sampled data",
"id": "2303.06045",
"abstract": "sampling in control applications is increasingly done non-equidistantly in time. this includes applications in motion control, networked control, resource-aware control, and event-based control. some of these applications, like the ones where displacement is tracked using incremental encoders, are driven by signals that are only measured when their values cross fixed thresholds in the amplitude domain. this paper introduces a non-parametric estimator of the impulse response and transfer function of continuous-time systems based on such amplitude-equidistant sampling strategy, known as lebesgue sampling. to this end, kernel methods are developed to formulate an algorithm that adequately takes into account the bounded output uncertainty between the event timestamps, which ultimately leads to more accurate models and more efficient output sampling compared to the equidistantly-sampled kernel-based approach. the efficacy of our proposed method is demonstrated through a mass-spring damper example with encoder measurements and extensive monte carlo simulation studies on system benchmarks.",
"categories": "eess.sy cs.sy",
"doi": "",
"created": "2023-03-10",
"updated": "2024-02-23",
"authors": [
"rodrigo a. gonz\u00e1lez",
"koen tiels",
"tom oomen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.06045"
} | "2024-03-15T03:38:24.648127" | {
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} | [] | "algorithm" | "1863a5a0-eb65-4a76-9517-b59c05e77190" | 1211 | hard |
|
\begin{algorithmic}[1]
\Require{$\{(A_i,Y_i)\}_{i=1}^m$ and $c \in [0,1]$}{}
\For{$u \in V$ }
\State $X_i=A_{i}[u,\cdot]$
\State $\beta(u) = Dcor(\{X_i, Y_i\}_{i=1}^m )$
\EndFor
\State $\hat{S} = \{u \in V| \beta(u) > c\}$.
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require{$\{(A_i,Y_i)\}_{i=1}^m$ and $c \in [0,1]$}{}
\For{$u \in V$ }
\State $X_i=A_{i}[u,\cdot]$
\State $\beta(u) = Dcor(\{X_i, Y_i\}_{i=1}^m )$
\EndFor
\State $\hat{S} = \{u \in V| \beta(u) > c\}$.
\end{algorithmic} | "https://arxiv.org/src/1801.07683" | "1801.07683.tar.gz" | "2024-02-05" | {
"title": "discovering the signal subgraph: an iterative screening approach on graphs",
"id": "1801.07683",
"abstract": "supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. existing conventional methods designed for euclidean data do not account for this graph dependency structure. to address this issue, this paper proposes an iterative vertex screening method to identify the signal subgraph that is most informative for the given graph attributes. the method screens the rows and columns of the adjacency matrix concurrently and stops when the resulting distance correlation is maximized. we establish the theoretical foundation of our method by proving that it estimates the true signal subgraph with high probability. additionally, we establish the convergence rate of classification error under the erdos-renyi random graph model and prove that the subsequent classification can be asymptotically optimal, outperforming the entire graph under high-dimensional conditions. our method is evaluated on various simulated datasets and real-world human and murine graphs derived from functional and structural magnetic resonance images. the results demonstrate its excellent performance in estimating the ground-truth signal subgraph and achieving superior classification accuracy.",
"categories": "stat.me",
"doi": "",
"created": "2018-01-23",
"updated": "2024-02-05",
"authors": [
"cencheng shen",
"shangsi wang",
"alexandra badea",
"carey e. priebe",
"joshua t. vogelstein"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1801.07683"
} | "2024-03-15T06:55:05.801196" | {
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} | [] | "algorithm" | "12f11cf2-05ea-4e5c-a672-27103ff98ca7" | 242 | easy |
|
\begin{algorithmic} % enter the algorithmic environment
\State Pick an initial state $(x_0,y_0,z_0) \sim \nu(x,y,z)$.
\For{$i = 0, 1, 2, \dots$}
\State Generate a random candidate state $(x', y', z') \sim \nu(x,y,z)$.
\State Calculate the acceptance probability $A(x_i, y_i, z_i, x', y', z') = \min\left\{1, \frac{\pi(x',y',z')\nu(x_i,y_i,z_i)}{\pi(x_i,y_i,z_i)\nu(x',y',z')}\right\}$
\State Generate a uniform random number $u \in [0,1]$.
\If{$u \le A(x_i,y_i,z_i, x', y', z')$}
\State accept the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x',y',z')$.
\Else
\State reject the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x_i, y_i, z_i)$.
\EndIf
\EndFor
\end{algorithmic}
| \begin{algorithmic}
% enter the algorithmic environment
\State Pick an initial state $(x_0,y_0,z_0) \sim \nu(x,y,z)$.
\For{$i = 0, 1, 2, \dots$}
\State Generate a random candidate state $(x', y', z') \sim \nu(x,y,z)$.
\State Calculate the acceptance probability $A(x_i, y_i, z_i, x', y', z') = \min\left\{1, \frac{\pi(x',y',z')\nu(x_i,y_i,z_i)}{\pi(x_i,y_i,z_i)\nu(x',y',z')}\right\}$
\State Generate a uniform random number $u \in [0,1]$.
\If{$u \le A(x_i,y_i,z_i, x', y', z')$}
\State accept the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x',y',z')$.
\Else
\State reject the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x_i, y_i, z_i)$.
\EndIf
\EndFor
\end{algorithmic} | "https://arxiv.org/src/1805.10721" | "1805.10721.tar.gz" | "2024-01-11" | {
"title": "bernstein's inequalities for general markov chains",
"id": "1805.10721",
"abstract": "we establish bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) markov chains. these inequalities achieve sharp variance proxies and encompass the classical bernstein inequality for independent random variables as special cases. the key analysis lies in bounding the operator norm of a perturbed markov transition kernel by the exponential of sum of two convex functions. one coincides with what delivers the classical bernstein inequality, and the other reflects the influence of the markov dependence. a convex analysis on these two functions then derives our bernstein inequalities. as applications, we apply our bernstein inequalities to the markov chain monte carlo integral estimation problem and the robust mean estimation problem with markov-dependent samples, and achieve tight deviation bounds that previous inequalities can not.",
"categories": "math.st stat.th",
"doi": "",
"created": "2018-05-27",
"updated": "2024-01-11",
"authors": [
"bai jiang",
"qiang sun",
"jianqing fan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1805.10721"
} | "2024-03-15T06:32:05.168692" | {
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} | [] | "algorithm" | "869ae36f-ec88-4a03-85c6-d8e631af69fa" | 709 | easy |
|
\begin{algorithm}[]
\caption{Signal Proportion Estimator}\label{alg}
\begin{algorithmic}[1]
\Statex {\bf Input:} $p$-values of the observed test statistics and bounding sequences $c_{m, 0.5}$ and $c_{m, 1}$
\Statex {\bf Output:} a proportion estimate $\hat \pi$
\State Rank the variables by their $p$-values so that $p_{(1)} < p_{(2)} < \ldots < p_{(m)}$
\State Compute
\[
\hat{\pi}_{0.5}= \max_{1 < j < m}\frac{ j/m-p_{(j)}-c_{m,0.5} \cdot \sqrt{p_{(j)}}} {1-p_{(j)}} \qquad \mbox{and} \qquad \hat{\pi}_{1}= \max_{1 < j < m}\frac{ j/m-p_{(j)} -c_{m,1} \cdot p_{(j)}} {1-p_{(j)}}
\]
\State Obtain $\hat \pi = \max\{\hat{\pi}_{0.5}, \hat{\pi}_{1}\}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[]
\caption{Signal Proportion Estimator} \begin{algorithmic}
[1]
\Statex {\bf Input:} $p$-values of the observed test statistics and bounding sequences $c_{m, 0.5}$ and $c_{m, 1}$
\Statex {\bf Output:} a proportion estimate $\hat \pi$
\State Rank the variables by their $p$-values so that $p_{(1)} < p_{(2)} < \ldots < p_{(m)}$
\State Compute
\[
\hat{\pi}_{0.5}= \max_{1 < j < m}\frac{ j/m-p_{(j)}-c_{m,0.5} \cdot \sqrt{p_{(j)}}} {1-p_{(j)}} \qquad \mbox{and} \qquad \hat{\pi}_{1}= \max_{1 < j < m}\frac{ j/m-p_{(j)} -c_{m,1} \cdot p_{(j)}} {1-p_{(j)}}
\]
\State Obtain $\hat \pi = \max\{\hat{\pi}_{0.5}, \hat{\pi}_{1}\}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2212.13574" | "2212.13574.tar.gz" | "2024-02-02" | {
"title": "weak signal inclusion under dependence and applications in genome-wide association study",
"id": "2212.13574",
"abstract": "motivated by the inquiries of weak signals in underpowered genome-wide association studies (gwass), we consider the problem of retaining true signals that are not strong enough to be individually separable from a large amount of noise. we address the challenge from the perspective of false negative control and present false negative control (fnc) screening, a data-driven method to efficiently regulate false negative proportion at a user-specified level. fnc screening is developed in a realistic setting with arbitrary covariance dependence between variables. we calibrate the overall dependence through a parameter whose scale is compatible with the existing phase diagram in high-dimensional sparse inference. utilizing the new calibration, we asymptotically explicate the joint effect of covariance dependence, signal sparsity, and signal intensity on the proposed method. we interpret the results using a new phase diagram, which shows that fnc screening can efficiently select a set of candidate variables to retain a high proportion of signals even when the signals are not individually separable from noise. finite sample performance of fnc screening is compared to those of several existing methods in simulation studies. the proposed method outperforms the others in adapting to a user-specified false negative control level. we implement fnc screening to empower a two-stage gwas procedure, which demonstrates substantial power gain when working with limited sample sizes in real applications.",
"categories": "stat.me",
"doi": "",
"created": "2022-12-27",
"updated": "2024-02-02",
"authors": [
"x. jessie jeng",
"yifei hu",
"quan sun",
"yun li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.13574"
} | "2024-03-15T07:22:29.819002" | {
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"_config.yml": {
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} | [] | "algorithm" | "85eaac21-1a19-47ec-854c-a3876e72f479" | 673 | easy |
|
\begin{algorithmic}[1]
\State \textbf{Input:} Query vector $q$; user-specified radius $R$; output from Algorithm~\ref{algo:index}
\State Compute $x_q: = q - \mu$
\State Compute the sorting score of $x_q$, i.e., $\alpha_q := x_q^T v_1$
\State Select candidate index range $J$ so that $|\alpha_j - \alpha_q| \le R$ for all $j\in J$
\State Compute $d := \overline{x}(J) - X(J,:)^T x_q$ using the precomputed $ \overline{x} = [\overline{x_i}]$
\State \textbf{Return:} Points $x_j$ with $d_j \leq (R^2 - x_q^T x_q)/2$ according to \eqref{eq:ip2}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input:} Query vector $q$; user-specified radius $R$; output from Algorithm~\ref{algo:index}
\State Compute $x_q: = q - \mu$
\State Compute the sorting score of $x_q$, i.e., $\alpha_q := x_q^T v_1$
\State Select candidate index range $J$ so that $|\alpha_j - \alpha_q| \le R$ for all $j\in J$
\State Compute $d := \overline{x}(J) - X(J,:)^T x_q$ using the precomputed $ \overline{x} = [\overline{x_i}]$
\State \textbf{Return:} Points $x_j$ with $d_j \leq (R^2 - x_q^T x_q)/2$ according to \eqref{eq:ip2}
\end{algorithmic} | "https://arxiv.org/src/2212.07679" | "2212.07679.tar.gz" | "2024-01-29" | {
"title": "fast and exact fixed-radius neighbor search based on sorting",
"id": "2212.07679",
"abstract": "fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. there are efficient algorithms that can provide fast approximate query responses, but they often have a very compute-intensive indexing phase and require careful parameter tuning. therefore, exact brute force and tree-based search methods are still widely used. here we propose a new fixed-radius near neighbor search method, called snn, that significantly improves over brute force and tree-based methods in terms of index and query time, provably returns exact results, and requires no parameter tuning. snn exploits a sorting of the data points by their first principal component to prune the query search space. further speedup is gained from an efficient implementation using high-level basic linear algebra subprograms (blas). we provide theoretical analysis of our method and demonstrate its practical performance when used stand-alone and when applied within the dbscan clustering algorithm.",
"categories": "cs.ir cs.ds",
"doi": "",
"created": "2022-12-15",
"updated": "2024-01-29",
"authors": [
"xinye chen",
"stefan g\u00fcttel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2212.07679"
} | "2024-03-15T08:42:59.915070" | {
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} | [] | "algorithm" | "0e5fcf47-636c-43fc-a429-da0dfb113895" | 559 | easy |
|
\begin{algorithm}
\caption{PC Sampling (HFS-SDE).}
\label{alg:PC Sampling-HFS}
\begin{algorithmic}[1]
\Require{$\{\beta_i\}_{i=1}^N, \{\alpha_i\}_{i=1}^N, \text{csm}, \mathbf{\hat{y}}, \lambda_1, \lambda_2, r, N, M, \mathbf{M_u}$.} \Comment{$\text{csm} = \{\text{csm}_1, \cdots, \text{csm}_n\}$, $M_u$ is the undersampling mask}
\State{$\mathbf{x}_{N} \sim \mathcal{N}(\mathbf{F}^{-1}(\mathbf{M}_l\mathbf{y}), \boldsymbol{\mathcal{F}}_h)$}
\For{$i = N-1$ to $0$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta^*}}\left(\mathbf{x}_{i+1}, i+1\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon \leftarrow \lambda_1\left(\|\mathbf{g}\|_{2} /\|\mathbf{G}\|_{2}\right)$}
\State{$\mathbf{x}_{i} \leftarrow \mathbf{x}_{i+1}+\dfrac{1}{2}\beta_{i+1}\boldsymbol{\mathcal{F}}_h(\mathbf{x}_i)+\beta_{i+1}(\mathbf{g}-\epsilon\mathbf{G})+\sqrt{\beta_{i+1}}\boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\For{$k \gets 1$ to $M$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta}^*}\left(\mathbf{x}_{i}^{k-1}, i\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i^k) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon_1 \leftarrow 2 \alpha_{i}\left(r\|\mathbf{z}\|_{2} /\|\mathbf{g}\|_{2}\right)^{2}$}
\State{$\epsilon_2 \leftarrow \|\mathbf{g}\|_{2} /(\lambda_2 \cdot \|\mathbf{G}\|_{2})$}
\State{$\mathbf{x}_{i}^{k} \leftarrow \mathbf{x}_{i}^{k-1}+\epsilon_1 (\mathbf{g}-\epsilon_2\mathbf{G})+\sqrt{2 \epsilon_1} \boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\EndFor
\State{$\mathbf{x}_{i-1}^{0} \leftarrow \mathbf{x}_{i}^{M}$}
\EndFor
\item[]
\Return{${\mathbf{x}}_0^0$} \Comment{$\mathbf{x}_0 = \mathbf{x}_i^0$}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{PC Sampling (HFS-SDE).}
\begin{algorithmic}
[1]
\Require{$\{\beta_i\}_{i=1}^N, \{\alpha_i\}_{i=1}^N, \text{csm}, \mathbf{\hat{y}}, \lambda_1, \lambda_2, r, N, M, \mathbf{M_u}$.} \Comment{$\text{csm} = \{\text{csm}_1, \cdots, \text{csm}_n\}$, $M_u$ is the undersampling mask}
\State{$\mathbf{x}_{N} \sim \mathcal{N}(\mathbf{F}^{-1}(\mathbf{M}_l\mathbf{y}), \boldsymbol{\mathcal{F}}_h)$}
\For{$i = N-1$ to $0$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta^*}}\left(\mathbf{x}_{i+1}, i+1\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon \leftarrow \lambda_1\left(\|\mathbf{g}\|_{2} /\|\mathbf{G}\|_{2}\right)$}
\State{$\mathbf{x}_{i} \leftarrow \mathbf{x}_{i+1}+\dfrac{1}{2}\beta_{i+1}\boldsymbol{\mathcal{F}}_h(\mathbf{x}_i)+\beta_{i+1}(\mathbf{g}-\epsilon\mathbf{G})+\sqrt{\beta_{i+1}}\boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\For{$k \gets 1$ to $M$}
\State{$\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$}
\State{$\mathbf{g} \leftarrow \boldsymbol{\mathcal{F}}_h(\mathbf{s}_{\boldsymbol{\theta}^*}\left(\mathbf{x}_{i}^{k-1}, i\right)$})
\State{$\mathbf{G}=\sum_{j=1}^{n} \text{csm}_j^{*} \cdot \mathbf{F}^{-1}\left(\mathbf{F}(\text{csm} \cdot \mathbf{x}_i^k) \cdot \mathbf{M_u} - \mathbf{\hat{y}}\right)$}
\State{$\epsilon_1 \leftarrow 2 \alpha_{i}\left(r\|\mathbf{z}\|_{2} /\|\mathbf{g}\|_{2}\right)^{2}$}
\State{$\epsilon_2 \leftarrow \|\mathbf{g}\|_{2} /(\lambda_2 \cdot \|\mathbf{G}\|_{2})$}
\State{$\mathbf{x}_{i}^{k} \leftarrow \mathbf{x}_{i}^{k-1}+\epsilon_1 (\mathbf{g}-\epsilon_2\mathbf{G})+\sqrt{2 \epsilon_1} \boldsymbol{\mathcal{F}}_h(\mathbf{z})$}
\EndFor
\State{$\mathbf{x}_{i-1}^{0} \leftarrow \mathbf{x}_{i}^{M}$}
\EndFor
\item[]
\Return{${\mathbf{x}}_0^0$} \Comment{$\mathbf{x}_0 = \mathbf{x}_i^0$}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2208.05481" | "2208.05481.tar.gz" | "2024-01-20" | {
"title": "high-frequency space diffusion models for accelerated mri",
"id": "2208.05481",
"abstract": "diffusion models with continuous stochastic differential equations (sdes) have shown superior performances in image generation. it can serve as a deep generative prior to solving the inverse problem in magnetic resonance (mr) reconstruction. however, low-frequency regions of $k$-space data are typically fully sampled in fast mr imaging, while existing diffusion models are performed throughout the entire image or $k$-space, inevitably introducing uncertainty in the reconstruction of low-frequency regions. additionally, existing diffusion models often demand substantial iterations to converge, resulting in time-consuming reconstructions. to address these challenges, we propose a novel sde tailored specifically for mr reconstruction with the diffusion process in high-frequency space (referred to as hfs-sde). this approach ensures determinism in the fully sampled low-frequency regions and accelerates the sampling procedure of reverse diffusion. experiments conducted on the publicly available fastmri dataset demonstrate that the proposed hfs-sde method outperforms traditional parallel imaging methods, supervised deep learning, and existing diffusion models in terms of reconstruction accuracy and stability. the fast convergence properties are also confirmed through theoretical and experimental validation. our code and weights are available at https://github.com/aboriginer/hfs-sde.",
"categories": "eess.iv cs.cv cs.lg",
"doi": "10.1109/tmi.2024.3351702",
"created": "2022-08-10",
"updated": "2024-01-20",
"authors": [
"chentao cao",
"zhuo-xu cui",
"yue wang",
"shaonan liu",
"taijin chen",
"hairong zheng",
"dong liang",
"yanjie zhu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2208.05481"
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|
\begin{algorithm}[H]
\caption{deep SMP-BSDE algorithm}
\begin{algorithmic}[1]
\State \textbf{Input:} Initial parameters $\left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1}\right)$, learning rate $\eta$; batch size $M$; number of iteration $K$.
\State \textbf{Data:} Simulated Brownian increments $\left\{ \Delta W_{t_i, k} \right\}_{0\leq i\leq N-1, 1\leq k\leq K}$
\State \textbf{Output:} The triple $(X_{t_i}, P_{t_i}, Q_{t_i})$
\For{$k = 1$ to $K$}
\State $X_{t_0, k}^{\pi} = x_0$, $P_{t_0, k}^{\pi} = \mu_0^\pi(x_0; \theta^P_{0} ) $
\For{$i = 0$ to $N-1$}
\State $ Q_{t_i, k}^{\pi} = \phi_i^\pi\left(X_{t_i}^\pi; \theta^Q_{i}\right) $
\State $ u_{t_i, k}^{\pi} = \mathcal{M}\left(t_i, X_{t_i, k}^{\pi}, P_{t_i,k}^{\pi}, Q_{t_i,k}^{\pi} \right)$
\State $ X_{t_{i+1},k}^{\pi} = X_{t_i,k}^{\pi} + \bar{b} \left(t_i, X_{t_i,k}^{\pi},u_{t_i, k}^{\pi} \right) \Delta t_i + \bar{\sigma} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta W_{t_i, k} $
\State $ P_{t_{i+1},k}^{\pi} = P_{t_i,k}^{\pi} - \bar{F} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta t_i + Q_{t_i,k}^{\pi} \Delta W_{t_i, k} $
\EndFor
\State $\text{Loss} = \frac{1}{M} \sum_{j=1}^M \left\| -\nabla_x g\left( X_{t_N,k}^{\pi} \right) - P_{t_N,k}^{\pi}\right\|^2 $
\State $ \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) \longleftarrow \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) - \eta \nabla \text{Loss} $
\EndFor
\end{algorithmic}
\label{algorithm}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{deep SMP-BSDE algorithm}
\begin{algorithmic}[1]
\State \textbf{Input:} Initial parameters $\left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1}\right)$, learning rate $\eta$; batch size $M$; number of iteration $K$.
\State \textbf{Data:} Simulated Brownian increments $\left\{ \Delta W_{t_i, k} \right\}_{0\leq i\leq N-1, 1\leq k\leq K}$
\State \textbf{Output:} The triple $(X_{t_i}, P_{t_i}, Q_{t_i})$
\For{$k = 1$ to $K$}
\State $X_{t_0, k}^{\pi} = x_0$, $P_{t_0, k}^{\pi} = \mu_0^\pi(x_0; \theta^P_{0} ) $
\For{$i = 0$ to $N-1$}
\State $ Q_{t_i, k}^{\pi} = \phi_i^\pi\left(X_{t_i}^\pi; \theta^Q_{i}\right) $
\State $ u_{t_i, k}^{\pi} = \mathcal{M}\left(t_i, X_{t_i, k}^{\pi}, P_{t_i,k}^{\pi}, Q_{t_i,k}^{\pi} \right)$
\State $ X_{t_{i+1},k}^{\pi} = X_{t_i,k}^{\pi} + \bar{b} \left(t_i, X_{t_i,k}^{\pi},u_{t_i, k}^{\pi} \right) \Delta t_i + \bar{\sigma} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta W_{t_i, k} $
\State $ P_{t_{i+1},k}^{\pi} = P_{t_i,k}^{\pi} - \bar{F} \left(t_i, X_{t_i,k}^{\pi}, u_{t_i, k}^{\pi} \right) \Delta t_i + Q_{t_i,k}^{\pi} \Delta W_{t_i, k} $
\EndFor
\State $\text{Loss} = \frac{1}{M} \sum_{j=1}^M \left\| -\nabla_x g\left( X_{t_N,k}^{\pi} \right) - P_{t_N,k}^{\pi}\right\|^2 $
\State $ \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) \longleftarrow \left(\theta^P_0, \theta^Q_0,\ldots, \theta^Q_{N-1} \right) - \eta \nabla \text{Loss} $
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.17472" | "2401.17472.tar.gz" | "2024-01-30" | {
"title": "convergence of the deep bsde method for stochastic control problems formulated through the stochastic maximum principle",
"id": "2401.17472",
"abstract": "it is well-known that decision-making problems from stochastic control can be formulated by means of forward-backward stochastic differential equation (fbsde). recently, the authors of ji et al. 2022 proposed an efficient deep learning-based algorithm which was based on the stochastic maximum principle (smp). in this paper, we provide a convergence result for this deep smp-bsde algorithm and compare its performance with other existing methods. in particular, by adopting a similar strategy as in han and long 2020, we derive a posteriori error estimate, and show that the total approximation error can be bounded by the value of the loss functional and the discretization error. we present numerical examples for high-dimensional stochastic control problems, both in case of drift- and diffusion control, which showcase superior performance compared to existing algorithms.",
"categories": "math.oc cs.na math.na q-fin.cp",
"doi": "",
"created": "2024-01-30",
"updated": "",
"authors": [
"zhipeng huang",
"balint negyesi",
"cornelis w. oosterlee"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.17472"
} | "2024-03-15T05:11:50.224129" | {
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|
\begin{algorithm}[t]
\caption{MEP-ONMF}
\label{alg}
\begin{algorithmic}[1]
\Require data matrix $X \in \mathbb{R}^{d \times n}_+$, number of features $k_{\text{max}}$, $\Gamma$, $\beta_{\text{max}}$, $c_j$ [for the $\ell_0$-forced version]
\State \textbf{Initialization} $\beta_{init}$%\leftarrow\frac{1}{2\lambda_{\text{max}}C_{x}}$
, $k\leftarrow1$, $w_1\leftarrow\sum_{x}xp(x)$, $\lambda_1\leftarrow1$, if $W$-orthogonal $X \leftarrow X^{\intercal}$
\State \textbf{Normalization} $x_j \leftarrow \frac{x_i}{||x_i||_2} \;$ for $i=1...n$
\Loop \, {until $\beta=\beta_{\text{max}}$}
\Repeat
\State update $p_{j|i}$, $w_j$ and $\alpha_j$ by (\ref{Gibbs}) and (\ref{alpha}) [or (\ref{optsol}) for optimally-weighted]
\Until convergence
\State $\beta \leftarrow \Gamma \beta$
\If{$k<k_{\text{max}}$}
\For {all $w_j$}
\State check the phase transition condition
\If{satisfied for $w_t$}
\State add another feature $w_{k+1}=w_t+\delta$
\State $\lambda_{w_{k+1}}\leftarrow0.5\lambda_{w_t}$, $\lambda_{w_t} \leftarrow 0.5\lambda_{w_t}$
\EndIf
\EndFor
\EndIf
\EndLoop
\State do post-processing (\ref{postpro}) on $H$
\State $W_{:j}\leftarrow w_j$ and $H_{ij}\leftarrow p_{j|i}$ $\forall i,j$
\State if {$W$-orthogonal}: $W\leftarrow H^{\intercal}$, $H\leftarrow W^{\intercal}$\\
\Return $W$, $H$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[t]
\caption{MEP-ONMF}
\begin{algorithmic}
[1]
\Require data matrix $X \in \mathbb{R}^{d \times n}_+$, number of features $k_{\text{max}}$, $\Gamma$, $\beta_{\text{max}}$, $c_j$ [for the $\ell_0$-forced version]
\State \textbf{Initialization} $\beta_{init}$%\leftarrow\frac{1}{2\lambda_{\text{max}}C_{x}}$
, $k\leftarrow1$, $w_1\leftarrow\sum_{x}xp(x)$, $\lambda_1\leftarrow1$, if $W$-orthogonal $X \leftarrow X^{\intercal}$
\State \textbf{Normalization} $x_j \leftarrow \frac{x_i}{||x_i||_2} \;$ for $i=1...n$
\Loop \, {until $\beta=\beta_{\text{max}}$}
\Repeat
\State update $p_{j|i}$, $w_j$ and $\alpha_j$ by (\ref{Gibbs}) and (\ref{alpha}) [or (\ref{optsol}) for optimally-weighted]
\Until convergence
\State $\beta \leftarrow \Gamma \beta$
\If{$k<k_{\text{max}}$}
\For {all $w_j$}
\State check the phase transition condition
\If{satisfied for $w_t$}
\State add another feature $w_{k+1}=w_t+\delta$
\State $\lambda_{w_{k+1}}\leftarrow0.5\lambda_{w_t}$, $\lambda_{w_t} \leftarrow 0.5\lambda_{w_t}$
\EndIf
\EndFor
\EndIf
\EndLoop
\State do post-processing (\ref{postpro}) on $H$
\State $W_{:j}\leftarrow w_j$ and $H_{ij}\leftarrow p_{j|i}$ $\forall i,j$
\State if {$W$-orthogonal}: $W\leftarrow H^{\intercal}$, $H\leftarrow W^{\intercal}$\\
\Return $W$, $H$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2210.02672" | "2210.02672.tar.gz" | "2024-01-18" | {
"title": "a novel maximum-entropy-driven technique for low-rank orthogonal nonnegative matrix factorization with $\\ell_0$-norm sparsity constraint",
"id": "2210.02672",
"abstract": "in data-driven control and machine learning, a common requirement involves breaking down large matrices into smaller, low-rank factors that possess specific levels of sparsity. this paper introduces an innovative solution to the orthogonal nonnegative matrix factorization (onmf) problem. the objective is to approximate input data by using two low-rank nonnegative matrices, adhering to both orthogonality and $\\ell_0$-norm sparsity constraints. the proposed maximum-entropy-principle based framework ensures orthogonality and sparsity of features or the mixing matrix, while maintaining nonnegativity in both. additionally, the methodology offers a quantitative determination of the ``true'' number of underlying features, a crucial hyperparameter for onmf. experimental evaluation on synthetic and a standard datasets highlights the method's superiority in terms of sparsity, orthogonality, and computational speed compared to existing approaches. notably, the proposed method achieves comparable or improved reconstruction errors in line with the literature.",
"categories": "cs.ds cs.it cs.lg math.it math.pr",
"doi": "",
"created": "2022-10-06",
"updated": "2024-01-18",
"authors": [
"salar basiri",
"srinivasa salapaka"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2210.02672"
} | "2024-03-15T05:57:43.061097" | {
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} | [] | "algorithm" | "db47442e-db5f-4ce3-b041-b23a0196675a" | 1311 | hard |
|
\begin{algorithm}
\caption{Terminal set construction via symbolic model}\label{safetygame}
\textbf{Input:} $\mathcal{X}$ (specification set), $\mathcal{D}_{N}$ (training dataset), $\eta_x, \eta_u, \varepsilon, \widetilde{\gamma}$ (some parameters for symbolic model), $\gamma_i$ for $i \in \mathbb{N}_{1: n_x}$ (a set of scalars);
\textbf{Output:} $\mathcal{X}_f$ (terminal set), $\mathcal{X}_S$ ($\tilde{\gamma}$-contractive set), $C$ (refined controller);
\begin{algorithmic}[1]
\State $\mathsf{q} \leftarrow (\eta_x, \eta_u, \varepsilon)$;\label{tripleline}
\State ${\Sigma}_{\mathsf{q}\tilde{\gamma}} \leftarrow (\mathcal{X}_{\mathsf{q}\tilde{\gamma}}, \mathcal{U}_{\mathsf{q}\tilde{\gamma}}, G_{\mathsf{q}\tilde{\gamma}})$;\label{symbolicline}
\State $\ell \leftarrow 0$;
\State $\mathcal{Q}_{\ell} \leftarrow \left[\bigcap_{i=1}^{n_x}\mathsf{Int}_{d_i}(\mathcal{X}; \epsilon_i)\right]_{{\eta}_x}$\label{finitestatesetline};
\Repeat\label{solvesafetygamestart}
\State $\mathcal{Q}_{\ell + 1} \leftarrow {\rm Pre}_{{\Sigma}_{\mathsf{q}\tilde{\gamma}}}(\mathcal{Q}_{\ell})$; \label{predecessoralg}
\State $\ell \leftarrow \ell + 1$;
\Until{$\mathcal{Q}_{\ell - 1} = \mathcal{Q}_{\ell}$;}\label{solvesafetygameend}
\State $\mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}} \leftarrow \mathcal{Q}_{\ell};$\label{compinvariantdisline}
\State $\mathcal{X}_S \leftarrow \{{x} \in \mathcal{X}: \ ({x}_{\mathsf{q}\tilde{\gamma}}, {x}) \in R(\varepsilon), \exists{x}_{\mathsf{q}\tilde{\gamma}} \in \mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}}\};$ \label{compinvariantline}
\State $C_{\mathsf{q}\tilde{\gamma}} \leftarrow \{{u}_{\mathsf{q}\tilde{\gamma}} \in \mathcal{U}_{\mathsf{q}\tilde{\gamma}}: \widetilde{G}({x}_{\mathsf{q}\tilde{\gamma}}, {u}_{\mathsf{q}\tilde{\gamma}}) \subseteq \mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}}, \ \forall {x}_{\mathsf{q}\tilde{\gamma}} \in \mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}}\};$\label{descontroller}
\State $C \leftarrow \{C_{\mathsf{q}\tilde{\gamma}}({x}_{\mathsf{q}\tilde{\gamma}}): ({x}_{\mathsf{q}\tilde{\gamma}}, {x}) \in R(\varepsilon), \ \forall {x} \in \mathcal{X}_S \}$; \label{refinecontroller}
\State $\mathcal{X}_f \leftarrow [\bigcap_{i=1}^{n_x}\mathsf{Int}_{\tilde{\gamma}_i}(\mathcal{X}_S), \bigcap_{i=1}^{n_x}\mathsf{Int}_{\gamma_i}(\mathcal{X}_S)]$;\label{terminalsetline}
\State \textbf{return} $\mathcal{X}_f, \mathcal{X}_S, C$;
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Terminal set construction via symbolic model}\textbf{Input:} $\mathcal{X}$ (specification set), $\mathcal{D}_{N}$ (training dataset), $\eta_x, \eta_u, \varepsilon, \widetilde{\gamma}$ (some parameters for symbolic model), $\gamma_i$ for $i \in \mathbb{N}_{1: n_x}$ (a set of scalars);
\textbf{Output:} $\mathcal{X}_f$ (terminal set), $\mathcal{X}_S$ ($\tilde{\gamma}$-contractive set), $C$ (refined controller);
\begin{algorithmic}
[1]
\State $\mathsf{q} \leftarrow (\eta_x, \eta_u, \varepsilon)$;
\State ${\Sigma}_{\mathsf{q}\tilde{\gamma}} \leftarrow (\mathcal{X}_{\mathsf{q}\tilde{\gamma}}, \mathcal{U}_{\mathsf{q}\tilde{\gamma}}, G_{\mathsf{q}\tilde{\gamma}})$;
\State $\ell \leftarrow 0$;
\State $\mathcal{Q}_{\ell} \leftarrow \left[\bigcap_{i=1}^{n_x}\mathsf{Int}_{d_i}(\mathcal{X}; \epsilon_i)\right]_{{\eta}_x}$;
\Repeat \State $\mathcal{Q}_{\ell + 1} \leftarrow {\rm Pre}_{{\Sigma}_{\mathsf{q}\tilde{\gamma}}}(\mathcal{Q}_{\ell})$; \State $\ell \leftarrow \ell + 1$;
\Until{$\mathcal{Q}_{\ell - 1} = \mathcal{Q}_{\ell}$;}
\State $\mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}} \leftarrow \mathcal{Q}_{\ell};$
\State $\mathcal{X}_S \leftarrow \{{x} \in \mathcal{X}: \ ({x}_{\mathsf{q}\tilde{\gamma}}, {x}) \in R(\varepsilon), \exists{x}_{\mathsf{q}\tilde{\gamma}} \in \mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}}\};$
\State $C_{\mathsf{q}\tilde{\gamma}} \leftarrow \{{u}_{\mathsf{q}\tilde{\gamma}} \in \mathcal{U}_{\mathsf{q}\tilde{\gamma}}: \widetilde{G}({x}_{\mathsf{q}\tilde{\gamma}}, {u}_{\mathsf{q}\tilde{\gamma}}) \subseteq \mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}}, \ \forall {x}_{\mathsf{q}\tilde{\gamma}} \in \mathcal{X}_{S, {\mathsf{q}\tilde{\gamma}}}\};$
\State $C \leftarrow \{C_{\mathsf{q}\tilde{\gamma}}({x}_{\mathsf{q}\tilde{\gamma}}): ({x}_{\mathsf{q}\tilde{\gamma}}, {x}) \in R(\varepsilon), \ \forall {x} \in \mathcal{X}_S \}$;
\State $\mathcal{X}_f \leftarrow [\bigcap_{i=1}^{n_x}\mathsf{Int}_{\tilde{\gamma}_i}(\mathcal{X}_S), \bigcap_{i=1}^{n_x}\mathsf{Int}_{\gamma_i}(\mathcal{X}_S)]$;
\State \textbf{return} $\mathcal{X}_f, \mathcal{X}_S, C$;
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2110.12214" | "2110.12214.tar.gz" | "2024-01-01" | {
"title": "learning-based event-triggered mpc with gaussian processes under terminal constraints",
"id": "2110.12214",
"abstract": "event-triggered control strategy is capable of significantly reducing the number of control task executions without sacrificing control performance. in this paper, we propose a novel learning-based approach towards an event-triggered model predictive control (mpc) for nonlinear control systems whose dynamics are unknown apriori. in particular, the optimal control problems (ocps) are formulated based on predictive states learned by gaussian process (gp) regression under a terminal constraint constructed by a symbolic abstraction. the event-triggered condition proposed in this paper is derived from the recursive feasibility so that the ocps are solved only when an error between the predictive and the actual states exceeds a certain threshold. based on the event-triggered condition, we analyze the stability of the closed-loop system and show that the finite-time convergence to the terminal set is achieved as the uncertainty of the gp model becomes smaller. moreover, in order to reduce the uncertainty of the gp model and increase efficiency to find the optimal solution, we provide an overall learning-based event-triggered mpc algorithm based on an iterative task. finally, we demonstrate the proposed approach through a tracking control problem.",
"categories": "math.oc",
"doi": "",
"created": "2021-10-23",
"updated": "2024-01-01",
"authors": [
"yuga onoue",
"kazumune hashimoto",
"akifumi wachi"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2110.12214"
} | "2024-03-15T07:05:39.786368" | {
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} | [] | "algorithm" | "450937fb-9168-43f8-91b6-6a7f464cc6c9" | 2132 | hard |
|
\begin{algorithm}[htbp] \label{ag:core}
\small
\caption{Training Process of RESTC}
\begin{algorithmic}[1]\label{ag:core}
\Require
Sessions $\mathbf{S}$, item embeddings $\mathbf{V_{s}}$
\Ensure
Top-k recommendation items
\State Transform session data into spatial and temporal view
\State Construct CFG overall sessions
\For{epoch in range(Epoches)}
\For{batch in DataLoader}
\For{each session s in batch}
\State \textbf{Spatio-Temporal Contrastive Learning task:}
\State Spatial view embedding $\mathbf{G}(s) \gets$ Eq.(1) to (6)
\State Temporal view embedding $\mathbf{T}(s) \gets$ Eq.(7) to (13)
\State Contrastive loss $\mathcal{L}_{cont} \gets$ Eq.(14)
\State \textbf{Prediction task:}
\State CFG embedding $\mathbf{\tilde{Z}} \gets$ Eq.(15)
\State Enhanced spatial embedding $\mathbf{H_{g}} \gets$ Eq.(16)
\State Embedding Fusion $\mathbf{S_{h}} \gets$ Eq.(17) to (19)
\State Next-item Predition loss $\mathcal{L}_{main} \gets$ Eq.(20), (21)
\EndFor
\EndFor
\State $\mathcal{L}=\mathcal{L}_{\text {main}}+\eta_{1} \mathcal{L}_{cont}+\eta_{2}\|\Theta\|_{2}^{2}$
\State Using multi-task training to jointly optimize $\mathcal{L}$
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}[htbp]
\small
\caption{Training Process of RESTC}
\begin{algorithmic}[1]
\Require
Sessions $\mathbf{S}$, item embeddings $\mathbf{V_{s}}$
\Ensure
Top-k recommendation items
\State Transform session data into spatial and temporal view
\State Construct CFG overall sessions
\For{epoch in range(Epoches)}
\For{batch in DataLoader}
\For{each session s in batch}
\State \textbf{Spatio-Temporal Contrastive Learning task:}
\State Spatial view embedding $\mathbf{G}(s) \gets$ Eq.(1) to (6)
\State Temporal view embedding $\mathbf{T}(s) \gets$ Eq.(7) to (13)
\State Contrastive loss $\mathcal{L}_{cont} \gets$ Eq.(14)
\State \textbf{Prediction task:}
\State CFG embedding $\mathbf{\tilde{Z}} \gets$ Eq.(15)
\State Enhanced spatial embedding $\mathbf{H_{g}} \gets$ Eq.(16)
\State Embedding Fusion $\mathbf{S_{h}} \gets$ Eq.(17) to (19)
\State Next-item Predition loss $\mathcal{L}_{main} \gets$ Eq.(20), (21)
\EndFor
\EndFor
\State $\mathcal{L}=\mathcal{L}_{\text {main}}+\eta_{1} \mathcal{L}_{cont}+\eta_{2}\|\Theta\|_{2}^{2}$
\State Using multi-task training to jointly optimize $\mathcal{L}$
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2209.11461" | "2209.11461.tar.gz" | "2024-02-17" | {
"title": "spatio-temporal contrastive learning enhanced gnns for session-based recommendation",
"id": "2209.11461",
"abstract": "session-based recommendation (sbr) systems aim to utilize the user's short-term behavior sequence to predict the next item without the detailed user profile. most recent works try to model the user preference by treating the sessions as between-item transition graphs and utilize various graph neural networks (gnns) to encode the representations of pair-wise relations among items and their neighbors. some of the existing gnn-based models mainly focus on aggregating information from the view of spatial graph structure, which ignores the temporal relations within neighbors of an item during message passing and the information loss results in a sub-optimal problem. other works embrace this challenge by incorporating additional temporal information but lack sufficient interaction between the spatial and temporal patterns. to address this issue, inspired by the uniformity and alignment properties of contrastive learning techniques, we propose a novel framework called session-based recommendation with spatio-temporal contrastive learning enhanced gnns (restc). the idea is to supplement the gnn-based main supervised recommendation task with the temporal representation via an auxiliary cross-view contrastive learning mechanism. furthermore, a novel global collaborative filtering graph (cfg) embedding is leveraged to enhance the spatial view in the main task. extensive experiments demonstrate the significant performance of restc compared with the state-of-the-art baselines e.g., with an improvement as much as 27.08% gain on hr@20 and 20.10% gain on mrr@20.",
"categories": "cs.ir",
"doi": "",
"created": "2022-09-23",
"updated": "2024-02-17",
"authors": [
"zhongwei wan",
"xin liu",
"benyou wang",
"jiezhong qiu",
"boyu li",
"ting guo",
"guangyong chen",
"yang wang"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2209.11461"
} | "2024-03-15T04:57:08.518692" | {
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} | [] | "algorithm" | "9911b2ea-f400-4613-936e-e4e5438295ee" | 1144 | medium |
|
\begin{algorithmic}[1]
\For{$b=1:N_m$}
\State (TV-AGRU)
\State Fix $\nu_M$ given by FIX-OPTIM.
\For{$j=1:N_{\text{tv}}$}
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$.
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\theta_{\text{AGRU}}$.
\State Update: $\theta_{\text{AGRU}} \gets \text{RMSProp}(\theta_{\text{AGRU}},\nabla_{\theta_{\text{AGRU}}} L,l_{\text{tv}})$.
\EndFor
\State (FIX-OPTIM)
\State Fix $\theta_{\text{AGRU}}$ given by TV-AGRU.
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$ and fix $\Theta^t_M$.
\For{$j=1:N_{\text{fix}}$}
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\nu_M$.
\State Update: $\nu_M \gets \text{RMSProp}(\nu_M,\nabla_{\nu_M} L,l_{\text{fix}})$.
\EndFor
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\For{$b=1:N_m$}
\State (TV-AGRU)
\State Fix $\nu_M$ given by FIX-OPTIM.
\For{$j=1:N_{\text{tv}}$}
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$.
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\theta_{\text{AGRU}}$.
\State Update: $\theta_{\text{AGRU}} \gets \text{RMSProp}(\theta_{\text{AGRU}},\nabla_{\theta_{\text{AGRU}}} L,l_{\text{tv}})$.
\EndFor
\State (FIX-OPTIM)
\State Fix $\theta_{\text{AGRU}}$ given by TV-AGRU.
\State Compute $\Theta^t_M = \{\alpha^t_M,\beta^t_M\} = \text{AGRU}(F_{<t};\theta_{\text{AGRU}})$ and fix $\Theta^t_M$.
\For{$j=1:N_{\text{fix}}$}
\State Compute the NLL loss $L=\sum_{t=1}^S (-\ell_M^t)$ and its partial derivatives with respect to $\nu_M$.
\State Update: $\nu_M \gets \text{RMSProp}(\nu_M,\nabla_{\nu_M} L,l_{\text{fix}})$.
\EndFor
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2301.07318" | "2301.07318.tar.gz" | "2024-01-16" | {
"title": "dynamic cvar portfolio construction with attention-powered generative factor learning",
"id": "2301.07318",
"abstract": "the dynamic portfolio construction problem requires dynamic modeling of the joint distribution of multivariate stock returns. to achieve this, we propose a dynamic generative factor model which uses random variable transformation as an implicit way of distribution modeling and relies on the attention-gru network for dynamic learning and forecasting. the proposed model captures the dynamic dependence among multivariate stock returns, especially focusing on the tail-side properties. we also propose a two-step iterative algorithm to train the model and then predict the time-varying model parameters, including the time-invariant tail parameters. at each investment date, we can easily simulate new samples from the learned generative model, and we further perform cvar portfolio optimization with the simulated samples to form a dynamic portfolio strategy. the numerical experiment on stock data shows that our model leads to wiser investments that promise higher reward-risk ratios and present lower tail risks.",
"categories": "q-fin.pm",
"doi": "",
"created": "2023-01-18",
"updated": "2024-01-16",
"authors": [
"chuting sun",
"qi wu",
"xing yan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2301.07318"
} | "2024-03-15T06:06:03.391456" | {
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} | [] | "algorithm" | "f5b6538c-e04d-444e-b226-68bfba511f0d" | 927 | medium |
|
\begin{algorithm}[H]
\caption{Our gradient estimation sampler}
\label{alg:second-order}
\begin{algorithmic}
\Require $(\sigma_N, \ldots, \sigma_0)$, $x_N \sim \mathcal{N}(0, I)$, $\epsilon_\theta$
\Ensure Compute $x_0$ with $N$ evaluations of $\epsilon_\theta$
\State $x_{N-1} \gets x_N + (\sigma_{N-1} - \sigma_N)\epsilon_\theta(x_N, \sigma_N)$
\For{$t = N-1, \ldots, 1$}
\State $\bar{\epsilon}_t \gets 2\epsilon_\theta(x_t, \sigma_t) - \epsilon_\theta(x_{t+1}, \sigma_{t+1})$
\State $x_{t-1} \gets x_t + (\sigma_{t-1} - \sigma_t) \bar{\epsilon}_t$
\EndFor
\State \Return $x_0$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Our gradient estimation sampler}
\begin{algorithmic}
\Require $(\sigma_N, \ldots, \sigma_0)$, $x_N \sim \mathcal{N}(0, I)$, $\epsilon_\theta$
\Ensure Compute $x_0$ with $N$ evaluations of $\epsilon_\theta$
\State $x_{N-1} \gets x_N + (\sigma_{N-1} - \sigma_N)\epsilon_\theta(x_N, \sigma_N)$
\For{$t = N-1, \ldots, 1$}
\State $\bar{\epsilon}_t \gets 2\epsilon_\theta(x_t, \sigma_t) - \epsilon_\theta(x_{t+1}, \sigma_{t+1})$
\State $x_{t-1} \gets x_t + (\sigma_{t-1} - \sigma_t) \bar{\epsilon}_t$
\EndFor
\State \Return $x_0$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2306.04848" | "2306.04848.tar.gz" | "2024-02-13" | {
"title": "interpreting and improving diffusion models using the euclidean distance function",
"id": "2306.04848",
"abstract": "denoising is intuitively related to projection. indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. hence, learning to denoise is approximately learning to project. in this paper, we use this observation to reinterpret denoising diffusion models as approximate gradient descent applied to the euclidean distance function. we then provide straight-forward convergence analysis of the ddim sampler under simple assumptions on the projection-error of the denoiser. finally, we propose a new sampler based on two simple modifications to ddim using insights from our theoretical results. in as few as 5-10 function evaluations, our sampler achieves state-of-the-art fid scores on pretrained cifar-10 and celeba models and can generate high quality samples on latent diffusion models.",
"categories": "cs.lg cs.cv math.oc stat.ml",
"doi": "",
"created": "2023-06-07",
"updated": "2024-02-13",
"authors": [
"frank permenter",
"chenyang yuan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2306.04848"
} | "2024-03-15T06:03:56.844522" | {
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} | [] | "algorithm" | "f3c57f48-601e-4ee5-b119-8948e83f714c" | 588 | easy |
|
\begin{algorithmic}[1]
\State \textbf{Input:} Each function has $W$ time points, then construct $Wp$-dimensional random vector ${f}$ ($W$: Full-time points) for $p$ functions, a set of its variable subscripts $U$ and a $Wp \times n$ data
matrix as $F$, initialize an ordered list of functions $K=\emptyset$ and $m:=1$;
\State \textbf{Output:} Adjacent Matrix $\hat{T}\in\mathbb{R}^{p\times p}$
\State Use FPCA for finite approximating each random vector to make their dimensions from $Wp$ to $Mp$, where $M$ is the number of principal components.
\Repeat
\State
(a) Perform least squares regressions of the approximating random vector $\hat{f}_{i}\in\mathbb{R}^M$ on $\hat{f}_{j}\in\mathbb{R}^M$ for all $ i \in U \backslash K(i \neq j) $ and compute the residual vectors $ \mathbf{r}^{(j)} $ and the residual data matrix $ \mathbf{R}^{(j)} $ from the data matrix $ {F} $ for all $ j \in U \backslash K $. Find a variable $ \hat{f}_{m} $ that is most independent of its residuals:
$$
\hat{f}_{m}=\arg \min _{j \in U \backslash K} MI\left(\hat{f}_{j} ; U \backslash K\right),
$$
where $ MI $ is the independence measure such as mutual information or other measures.
\State (b) Append $ m $ to the end of $ K $.
\State (c) Let $\hat{\mathbf{f}}:=\mathbf{r}^{(m)}, \hat{F}:=\mathbf{R}^{(m)} $.
\Until{$p-1$ subscripts are appended to $K$}
\State Append the remaining variable to the end of $ K $.
\State Construct a strictly lower triangular matrix $\hat{T} $ by following the order in $ K $, and estimate the connection strengths $ \hat{T}_{i j} $ by using least squares regression in this paper.
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input:} Each function has $W$ time points, then construct $Wp$-dimensional random vector ${f}$ ($W$: Full-time points) for $p$ functions, a set of its variable subscripts $U$ and a $Wp \times n$ data
matrix as $F$, initialize an ordered list of functions $K=\emptyset$ and $m:=1$;
\State \textbf{Output:} Adjacent Matrix $\hat{T}\in\mathbb{R}^{p\times p}$
\State Use FPCA for finite approximating each random vector to make their dimensions from $Wp$ to $Mp$, where $M$ is the number of principal components.
\Repeat
\State
(a) Perform least squares regressions of the approximating random vector $\hat{f}_{i}\in\mathbb{R}^M$ on $\hat{f}_{j}\in\mathbb{R}^M$ for all $ i \in U \backslash K(i \neq j) $ and compute the residual vectors $ \mathbf{r}^{(j)} $ and the residual data matrix $ \mathbf{R}^{(j)} $ from the data matrix $ {F} $ for all $ j \in U \backslash K $. Find a variable $ \hat{f}_{m} $ that is most independent of its residuals:
$$
\hat{f}_{m}=\arg \min _{j \in U \backslash K} MI\left(\hat{f}_{j} ; U \backslash K\right),
$$
where $ MI $ is the independence measure such as mutual information or other measures.
\State (b) Append $ m $ to the end of $ K $.
\State (c) Let $\hat{\mathbf{f}}:=\mathbf{r}^{(m)}, \hat{F}:=\mathbf{R}^{(m)} $.
\Until{$p-1$ subscripts are appended to $K$}
\State Append the remaining variable to the end of $ K $.
\State Construct a strictly lower triangular matrix $\hat{T} $ by following the order in $ K $, and estimate the connection strengths $ \hat{T}_{i j} $ by using least squares regression in this paper.
\end{algorithmic} | "https://arxiv.org/src/2401.09641" | "2401.09641.tar.gz" | "2024-01-17" | {
"title": "functional linear non-gaussian acyclic model for causal discovery",
"id": "2401.09641",
"abstract": "in causal discovery, non-gaussianity has been used to characterize the complete configuration of a linear non-gaussian acyclic model (lingam), encompassing both the causal ordering of variables and their respective connection strengths. however, lingam can only deal with the finite-dimensional case. to expand this concept, we extend the notion of variables to encompass vectors and even functions, leading to the functional linear non-gaussian acyclic model (func-lingam). our motivation stems from the desire to identify causal relationships in brain-effective connectivity tasks involving, for example, fmri and eeg datasets. we demonstrate why the original lingam fails to handle these inherently infinite-dimensional datasets and explain the availability of functional data analysis from both empirical and theoretical perspectives. {we establish theoretical guarantees of the identifiability of the causal relationship among non-gaussian random vectors and even random functions in infinite-dimensional hilbert spaces.} to address the issue of sparsity in discrete time points within intrinsic infinite-dimensional functional data, we propose optimizing the coordinates of the vectors using functional principal component analysis. experimental results on synthetic data verify the ability of the proposed framework to identify causal relationships among multivariate functions using the observed samples. for real data, we focus on analyzing the brain connectivity patterns derived from fmri data.",
"categories": "cs.lg math.st q-bio.nc stat.me stat.th",
"doi": "",
"created": "2024-01-17",
"updated": "",
"authors": [
"tian-le yang",
"kuang-yao lee",
"kun zhang",
"joe suzuki"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.09641"
} | "2024-03-15T07:19:39.274028" | {
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} | [] | "algorithm" | "c4695c9d-e7ff-4634-a8b4-f3e0281ce914" | 1613 | hard |
|
\begin{algorithm}[H]
\caption{Expansion ranges}
\label{alg:expansionrange}\begin{algorithmic}[1]
\State Input:
\begin{enumerate}
\item[1] Difference equation system $\Sigma$ with algebraic or analytic transcendental functions.
\item[2] For each parameter $\mu_i$ appearing as an argument of a transcendental function, user-specified acceptable domains for each $\mu_i$, denoted $R_{\mu_i}$.
\item[3] Observed data $\bar{y}(t_0),\bar{y}(t_1),\ldots,\bar{y}(t_r)$
\end{enumerate}
\State Output: Domains $R_{G_{j}}$ over which each transcendental function $G_j$ in $\Sigma$ is expanded.
\Procedure{Expansion range}{} By substitution of maximums and minimums (modulus) of \phantom{-----} $R_{\mu_i}$ into arguments of $G_j$, as relevant, determine radii of discs $R_{L_t}$.
\State Call the argument of $G_j$ as $\tilde{G}_j=:\tau_j$.
\For{$j=1\to r$, $t$ fixed}
\State $\displaystyle R_{G_{j,t}}:=\left\{\min_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\le |\tau_j| \le\max_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\right\}$
\EndFor
\EndProcedure
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Expansion ranges}
\begin{algorithmic}
[1]
\State Input:
\begin{enumerate}
\item[1] Difference equation system $\Sigma$ with algebraic or analytic transcendental functions.
\item[2] For each parameter $\mu_i$ appearing as an argument of a transcendental function, user-specified acceptable domains for each $\mu_i$, denoted $R_{\mu_i}$.
\item[3] Observed data $\bar{y}(t_0),\bar{y}(t_1),\ldots,\bar{y}(t_r)$
\end{enumerate}
\State Output: Domains $R_{G_{j}}$ over which each transcendental function $G_j$ in $\Sigma$ is expanded.
\Procedure{Expansion range}{} By substitution of maximums and minimums (modulus) of \phantom{-----} $R_{\mu_i}$ into arguments of $G_j$, as relevant, determine radii of discs $R_{L_t}$.
\State Call the argument of $G_j$ as $\tilde{G}_j=:\tau_j$.
\For{$j=1\to r$, $t$ fixed}
\State $\displaystyle R_{G_{j,t}}:=\left\{\min_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\le |\tau_j| \le\max_{R
_{\mu_i^*,i=1,\ldots,s} }|\tilde{G}_j|\right\}$
\EndFor
\EndProcedure
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.16220" | "2401.16220.tar.gz" | "2024-01-29" | {
"title": "symbolic-numeric algorithm for parameter estimation in discrete-time models with $\\exp$",
"id": "2401.16220",
"abstract": "determining unknown parameter values in dynamic models is crucial for accurate analysis of the dynamics across the different scientific disciplines. discrete-time dynamic models are widely used to model biological processes, but it is often difficult to determine these parameters. in this paper, we propose a robust symbolic-numeric approach for parameter estimation in discrete-time models that involve non-algebraic functions such as exp. we illustrate the performance (precision) of our approach by applying our approach to the flour beetle (lpa) model, an archetypal discrete-time model in biology. unlike optimization-based methods, our algorithm guarantees to find all solutions of the parameter values given time-series data for the measured variables.",
"categories": "q-bio.qm cs.sc cs.sy eess.sy math.ac math.ds",
"doi": "",
"created": "2024-01-29",
"updated": "",
"authors": [
"yosef berman",
"joshua forrest",
"matthew grote",
"alexey ovchinnikov",
"sonia rueda"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.16220"
} | "2024-03-15T06:38:23.919697" | {
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} | [] | "algorithm" | "adc38873-615d-489f-a7ba-a1c43e5cfe9c" | 1049 | medium |
|
\begin{algorithm}[t]
\caption{Constructing a pseudo-image from a whole genome sample for a given k-mer size $k$.}\label{alg:cap}
\begin{algorithmic}
\Require Sequence reads $X_i = \{X_0, X_1, \ldots X_N\}, \forall X_i \in \mathcal{X}_i$
\Ensure Pseudo-image $I_r$
\Procedure{relativeCoOccurrence}{$x_i, x_j$, $I_r$}
\State $e_{i,j} \gets I_r[i,j]$ \Comment{Current co-occurrence frequency}
\State $e^\prime_{i,j} \gets e_{i,j} + 1$ \Comment{New co-occurrence frequency}
\State $r \gets \frac{e_{i,j}}{(\Vert e_{i,j} - e^{\prime}_{i,j} \Vert_2)}$ \Comment{Update co-occurrence}
\State $e_{i,j} = 2 \sqrt{max(r - 1, 1)} + (min(r-2,2) + 2)$
\State \textbf{return} $e_{i,j}$\Comment{Relative co-occurrence frequency}
\EndProcedure
\Procedure{NormalizeImage}{$I_r, \lambda_m$}
\State $N\gets\sum_{i=0}^{4^k}{\sum_{j=0}^{4^k}{I[i,j]}}$
\For{$i \in 4^k$}
\For{$j \in 4^k$}
\If{$I_r[i,j] > \lambda_m$}
\State$I_r[i,j]\gets 255*I[i,j]/N$
\Else
\State$I_r[i,j]\gets 0$
\EndIf
\EndFor
\EndFor
\State \textbf{return} $I_r$\Comment{Normalized Pseudo-Image}
\EndProcedure
\State $I_r \gets ones(4^k,4^k)$ \Comment{Initial pseudo-image}
\For{$ X_i \in \mathcal{X}_i $} \Comment{Iterate through each sequence}
\For{$ x_i, x_j \in X_i $} \Comment{Iterate through successive k-mers}
\State $I_r[i,j]\gets$\Call{relativeCoOccurrence}{$x_i, x_j$, $I_r$}
\EndFor
\EndFor
\State $I_r\gets$ \Call{NormalizeImage}{$I_r, \lambda_m$}
\State \textbf{return} $I_r$\Comment{Final pseudo-image}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[t]
\caption{Constructing a pseudo-image from a whole genome sample for a given k-mer size $k$.}\begin{algorithmic}
\Require Sequence reads $X_i = \{X_0, X_1, \ldots X_N\}, \forall X_i \in \mathcal{X}_i$
\Ensure Pseudo-image $I_r$
\Procedure{relativeCoOccurrence}{$x_i, x_j$, $I_r$}
\State $e_{i,j} \gets I_r[i,j]$ \Comment{Current co-occurrence frequency}
\State $e^\prime_{i,j} \gets e_{i,j} + 1$ \Comment{New co-occurrence frequency}
\State $r \gets \frac{e_{i,j}}{(\Vert e_{i,j} - e^{\prime}_{i,j} \Vert_2)}$ \Comment{Update co-occurrence}
\State $e_{i,j} = 2 \sqrt{max(r - 1, 1)} + (min(r-2,2) + 2)$
\State \textbf{return} $e_{i,j}$\Comment{Relative co-occurrence frequency}
\EndProcedure
\Procedure{NormalizeImage}{$I_r, \lambda_m$}
\State $N\gets\sum_{i=0}^{4^k}{\sum_{j=0}^{4^k}{I[i,j]}}$
\For{$i \in 4^k$}
\For{$j \in 4^k$}
\If{$I_r[i,j] > \lambda_m$}
\State$I_r[i,j]\gets 255*I[i,j]/N$
\Else
\State$I_r[i,j]\gets 0$
\EndIf
\EndFor
\EndFor
\State \textbf{return} $I_r$\Comment{Normalized Pseudo-Image}
\EndProcedure
\State $I_r \gets ones(4^k,4^k)$ \Comment{Initial pseudo-image}
\For{$ X_i \in \mathcal{X}_i $} \Comment{Iterate through each sequence}
\For{$ x_i, x_j \in X_i $} \Comment{Iterate through successive k-mers}
\State $I_r[i,j]\gets$\Call{relativeCoOccurrence}{$x_i, x_j$, $I_r$}
\EndFor
\EndFor
\State $I_r\gets$ \Call{NormalizeImage}{$I_r, \lambda_m$}
\State \textbf{return} $I_r$\Comment{Final pseudo-image}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.13219" | "2401.13219.tar.gz" | "2024-01-23" | {
"title": "tepi: taxonomy-aware embedding and pseudo-imaging for scarcely-labeled zero-shot genome classification",
"id": "2401.13219",
"abstract": "a species' genetic code or genome encodes valuable evolutionary, biological, and phylogenetic information that aids in species recognition, taxonomic classification, and understanding genetic predispositions like drug resistance and virulence. however, the vast number of potential species poses significant challenges in developing a general-purpose whole genome classification tool. traditional bioinformatics tools have made notable progress but lack scalability and are computationally expensive. machine learning-based frameworks show promise but must address the issue of large classification vocabularies with long-tail distributions. in this study, we propose addressing this problem through zero-shot learning using tepi, taxonomy-aware embedding and pseudo-imaging. we represent each genome as pseudo-images and map them to a taxonomy-aware embedding space for reasoning and classification. this embedding space captures compositional and phylogenetic relationships of species, enabling predictions in extensive search spaces. we evaluate tepi using two rigorous zero-shot settings and demonstrate its generalization capabilities qualitatively on curated, large-scale, publicly sourced data.",
"categories": "q-bio.gn cs.ai cs.lg",
"doi": "",
"created": "2024-01-23",
"updated": "",
"authors": [
"sathyanarayanan aakur",
"vishalini r. laguduva",
"priyadharsini ramamurthy",
"akhilesh ramachandran"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.13219"
} | "2024-03-15T06:48:41.356948" | {
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} | [] | "algorithm" | "eeb16cae-98ff-4486-91cf-495a6c4ec7df" | 1483 | hard |
|
\begin{algorithmic}[1]
\Statex \textbf{Input:}\texttt{ Set of sequences(S)}
\Statex \textbf{Output:}\texttt{ Distance Matrix(D)}
\For{\texttt{ $s_{1}$ in S\hspace{0.2cm}}}
\State \texttt{ $Es_{1} \gets encoded \hspace{0.2cm} s_{1}$}
\State \texttt{ $Cs_{1} \gets Gzip\hspace{0.2cm} compressed \hspace{0.2cm} Es_{1}$}
\State \texttt{ $Ls_{1} \gets length \hspace{0.2cm} of \hspace{0.2cm} Cs_{1}$}
\State \texttt{ $D \_ local \gets [\ ]$}
\For{\texttt{ $s_{2}$ in S\hspace{0.2cm}}}
\State \texttt{ $Es_{2} \gets encoded \hspace{0.2cm} s_{2}$}
\State \texttt{ $Cs_{2} \gets Gzip \hspace{0.2cm} compressed \hspace{0.2cm} Es_{2}$}
\State \texttt{ $Ls_{2} \gets length \hspace{0.2cm} of \hspace{0.2cm} Cs_{2}$}
\State \texttt{ $s_{1}s_{2} \gets Concatenate(s_{1},s_{2})$}
\State \texttt{ $Es_{1}s_{2} \gets encoded \hspace{0.2cm} s_{1}s_{2}$}
\State \texttt{ $Cs_{1}s_{2} \gets Gzip \hspace{0.2cm} compressed \hspace{0.2cm} Es_{1}s_{2}$}
\State \texttt{ $Ls_{1}s_{2} \gets length \hspace{0.2cm} of \hspace{0.2cm} Cs_{1}s_{2}$}
\State NCD $\gets$ $\dfrac{L s_1 s_2 - Min (Ls_1, Ls_2)}{Max(Ls_1, Ls_2)}$
\State \texttt{ $D\_local.append(NCD)$}
\EndFor
\State $D.append(D\_local)$
\EndFor
\State return $D$
\end{algorithmic}
| \begin{algorithmic}
[1]
\Statex \textbf{Input:}\texttt{ Set of sequences(S)}
\Statex \textbf{Output:}\texttt{ Distance Matrix(D)}
\For{\texttt{ $s_{1}$ in S\hspace{0.2cm}}}
\State \texttt{ $Es_{1} \gets encoded \hspace{0.2cm} s_{1}$}
\State \texttt{ $Cs_{1} \gets Gzip\hspace{0.2cm} compressed \hspace{0.2cm} Es_{1}$}
\State \texttt{ $Ls_{1} \gets length \hspace{0.2cm} of \hspace{0.2cm} Cs_{1}$}
\State \texttt{ $D \_ local \gets [\ ]$}
\For{\texttt{ $s_{2}$ in S\hspace{0.2cm}}}
\State \texttt{ $Es_{2} \gets encoded \hspace{0.2cm} s_{2}$}
\State \texttt{ $Cs_{2} \gets Gzip \hspace{0.2cm} compressed \hspace{0.2cm} Es_{2}$}
\State \texttt{ $Ls_{2} \gets length \hspace{0.2cm} of \hspace{0.2cm} Cs_{2}$}
\State \texttt{ $s_{1}s_{2} \gets Concatenate(s_{1},s_{2})$}
\State \texttt{ $Es_{1}s_{2} \gets encoded \hspace{0.2cm} s_{1}s_{2}$}
\State \texttt{ $Cs_{1}s_{2} \gets Gzip \hspace{0.2cm} compressed \hspace{0.2cm} Es_{1}s_{2}$}
\State \texttt{ $Ls_{1}s_{2} \gets length \hspace{0.2cm} of \hspace{0.2cm} Cs_{1}s_{2}$}
\State NCD $\gets$ $\dfrac{L s_1 s_2 - Min (Ls_1, Ls_2)}{Max(Ls_1, Ls_2)}$
\State \texttt{ $D\_local.append(NCD)$}
\EndFor
\State $D.append(D\_local)$
\EndFor
\State return $D$
\end{algorithmic} | "https://arxiv.org/src/2402.08117" | "2402.08117.tar.gz" | "2024-02-12" | {
"title": "a universal non-parametric approach for improved molecular sequence analysis",
"id": "2402.08117",
"abstract": "in the field of biological research, it is essential to comprehend the characteristics and functions of molecular sequences. the classification of molecular sequences has seen widespread use of neural network-based techniques. despite their astounding accuracy, these models often require a substantial number of parameters and more data collection. in this work, we present a novel approach based on the compression-based model, motivated from \\cite{jiang2023low}, which combines the simplicity of basic compression algorithms like gzip and bz2, with normalized compression distance (ncd) algorithm to achieve better performance on classification tasks without relying on handcrafted features or pre-trained models. firstly, we compress the molecular sequence using well-known compression algorithms, such as gzip and bz2. by leveraging the latent structure encoded in compressed files, we compute the normalized compression distance between each pair of molecular sequences, which is derived from the kolmogorov complexity. this gives us a distance matrix, which is the input for generating a kernel matrix using a gaussian kernel. next, we employ kernel principal component analysis (pca) to get the vector representations for the corresponding molecular sequence, capturing important structural and functional information. the resulting vector representations provide an efficient yet effective solution for molecular sequence analysis and can be used in ml-based downstream tasks. the proposed approach eliminates the need for computationally intensive deep neural networks (dnns), with their large parameter counts and data requirements. instead, it leverages a lightweight and universally accessible compression-based model.",
"categories": "cs.lg q-bio.qm",
"doi": "",
"created": "2024-02-12",
"updated": "",
"authors": [
"sarwan ali",
"tamkanat e ali",
"prakash chourasia",
"murray patterson"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.08117"
} | "2024-03-15T04:40:32.096340" | {
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} | [] | "algorithm" | "232fef09-6702-461f-b049-5dffc6042b2c" | 1216 | hard |
|
\begin{algorithmic}[1]
\Require
Training set $\mathcal{D}$, validation set size $M_{\mathrm{val}}$, learning rate $\zeta$, training iteration $T$, PGD function for finding adversarial validation data.
\Ensure An infinite-width adversarially robust DNN.
\State Randomly separate $\mathcal D$ into subsets $\mathcal D_{\mathrm{opt}}$ and $\mathcal D_{\mathrm{val}}$ such that $| \mathcal D_{\mathrm{val}} | = M_{\mathrm{val}}$.
\State Initialize trainable parameter $\varpi_0 \in \mathbb{R}^{|\mathcal D_{\mathrm{val}}| \cdot c}$ with zeros.
\For{$t$ \textbf{in} $1, \cdots, T$}
\State Sample a minibatch $(x, y) \sim \mathcal D_{\mathrm{val}}$.
\State $x' \leftarrow \mathrm{PGD}(x,y,f_{\varpi_{t-1}})$
\Comment{Finding adversarial validation examples.}
\State $g_t \leftarrow \partial_{\varpi} \frac{1}{2} \| f_{\varpi_{t-1}}(x') - y \|_2^2$
\State $\varpi_t \leftarrow \varpi_{t-1} - \zeta \cdot \frac{g_t}{\|g_t\|_2}$
\Comment{Update model parameter via SGD and $\ell_2$-GardNorm.}
\EndFor
\State \Return $f_{\varpi_T}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require
Training set $\mathcal{D}$, validation set size $M_{\mathrm{val}}$, learning rate $\zeta$, training iteration $T$, PGD function for finding adversarial validation data.
\Ensure An infinite-width adversarially robust DNN.
\State Randomly separate $\mathcal D$ into subsets $\mathcal D_{\mathrm{opt}}$ and $\mathcal D_{\mathrm{val}}$ such that $| \mathcal D_{\mathrm{val}} | = M_{\mathrm{val}}$.
\State Initialize trainable parameter $\varpi_0 \in \mathbb{R}^{|\mathcal D_{\mathrm{val}}| \cdot c}$ with zeros.
\For{$t$ \textbf{in} $1, \cdots, T$}
\State Sample a minibatch $(x, y) \sim \mathcal D_{\mathrm{val}}$.
\State $x' \leftarrow \mathrm{PGD}(x,y,f_{\varpi_{t-1}})$
\Comment{Finding adversarial validation examples.}
\State $g_t \leftarrow \partial_{\varpi} \frac{1}{2} \| f_{\varpi_{t-1}}(x') - y \|_2^2$
\State $\varpi_t \leftarrow \varpi_{t-1} - \zeta \cdot \frac{g_t}{\|g_t\|_2}$
\Comment{Update model parameter via SGD and $\ell_2$-GardNorm.}
\EndFor
\State \Return $f_{\varpi_T}$
\end{algorithmic} | "https://arxiv.org/src/2310.06112" | "2310.06112.tar.gz" | "2024-02-04" | {
"title": "theoretical analysis of robust overfitting for wide dnns: an ntk approach",
"id": "2310.06112",
"abstract": "adversarial training (at) is a canonical method for enhancing the robustness of deep neural networks (dnns). however, recent studies empirically demonstrated that it suffers from robust overfitting, i.e., a long time at can be detrimental to the robustness of dnns. this paper presents a theoretical explanation of robust overfitting for dnns. specifically, we non-trivially extend the neural tangent kernel (ntk) theory to at and prove that an adversarially trained wide dnn can be well approximated by a linearized dnn. moreover, for squared loss, closed-form at dynamics for the linearized dnn can be derived, which reveals a new at degeneration phenomenon: a long-term at will result in a wide dnn degenerates to that obtained without at and thus cause robust overfitting. based on our theoretical results, we further design a method namely adv-ntk, the first at algorithm for infinite-width dnns. experiments on real-world datasets show that adv-ntk can help infinite-width dnns enhance comparable robustness to that of their finite-width counterparts, which in turn justifies our theoretical findings. the code is available at https://github.com/fshp971/adv-ntk.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2023-10-09",
"updated": "2024-02-04",
"authors": [
"shaopeng fu",
"di wang"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2310.06112"
} | "2024-03-15T07:33:05.157801" | {
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|
\begin{algorithm}
\caption{Credal Bayesian Deep Learning (CBDL) -- Training and Inference}\label{algo-1}
\begin{algorithmic}
\item
\textit{During Training}
\item
\textbf{Step 1} Specify $K$ priors $\text{ex}\mathcal{P}_\text{prior}=\{P^\text{ex}_k\}_{k=1}^K$
\item
\textbf{Step 2} Specify $S$ likelihoods $\text{ex}\mathcal{P}_\text{lik}=\{L^\text{ex}_s\}_{s=1}^S$
\item
\textbf{Step 3} Compute $P_{k,s}(\cdot \mid D)=\mathsf{post}[P_k^\text{ex},L_s^\text{ex}]$, for all $k$ and all $s$ \Comment{\% Approximated via VI by $\breve{P}_{k,s}$\%}
\item
\textit{During Inference}
\flushleft
\hspace*{\algorithmicindent} \textbf{Inputs:} New input $\tilde{x}\in\mathcal{X}$\\
\hspace*{\algorithmicindent} \textbf{Parameters:} Confidence parameter $\alpha \in [0,1]$
\\
\hspace*{\algorithmicindent} \textbf{Outputs:} Aleatoric and Epistemic Uncertainties, $\alpha$-level IHDR
\item
\textbf{Step 4} Compute ${P}^\text{pred}_{k,s}=\mathsf{pred}[\breve{P}_{k,s},L^\text{ex}_s]$, for all $k$ and all $s$ \Comment{\% Approximated via VI by $\hat{P}^\text{pred}_{k,s}$\%}
\item
\textbf{Step 5} Compute and return $\text{AU}(\hat{\mathcal{P}}_\text{pred})$ and the bounds for $\text{EU}(\hat{\mathcal{P}}_\text{pred})$
\item
\textbf{Step 6} Compute and return the $(1-\alpha)$-IHDR $IR_\alpha(\hat{\mathcal{P}}_\text{pred})$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Credal Bayesian Deep Learning (CBDL) -- Training and Inference}\begin{algorithmic}
\item
\textit{During Training}
\item
\textbf{Step 1} Specify $K$ priors $\text{ex}\mathcal{P}_\text{prior}=\{P^\text{ex}_k\}_{k=1}^K$
\item
\textbf{Step 2} Specify $S$ likelihoods $\text{ex}\mathcal{P}_\text{lik}=\{L^\text{ex}_s\}_{s=1}^S$
\item
\textbf{Step 3} Compute $P_{k,s}(\cdot \mid D)=\mathsf{post}[P_k^\text{ex},L_s^\text{ex}]$, for all $k$ and all $s$ \Comment{\% Approximated via VI by $\breve{P}_{k,s}$\%}
\item
\textit{During Inference}
\flushleft
\hspace*{\algorithmicindent} \textbf{Inputs:} New input $\tilde{x}\in\mathcal{X}$\\
\hspace*{\algorithmicindent} \textbf{Parameters:} Confidence parameter $\alpha \in [0,1]$
\\
\hspace*{\algorithmicindent} \textbf{Outputs:} Aleatoric and Epistemic Uncertainties, $\alpha$-level IHDR
\item
\textbf{Step 4} Compute ${P}^\text{pred}_{k,s}=\mathsf{pred}[\breve{P}_{k,s},L^\text{ex}_s]$, for all $k$ and all $s$ \Comment{\% Approximated via VI by $\hat{P}^\text{pred}_{k,s}$\%}
\item
\textbf{Step 5} Compute and return $\text{AU}(\hat{\mathcal{P}}_\text{pred})$ and the bounds for $\text{EU}(\hat{\mathcal{P}}_\text{pred})$
\item
\textbf{Step 6} Compute and return the $(1-\alpha)$-IHDR $IR_\alpha(\hat{\mathcal{P}}_\text{pred})$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2302.09656" | "2302.09656.tar.gz" | "2024-02-22" | {
"title": "credal bayesian deep learning",
"id": "2302.09656",
"abstract": "uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. although bayesian neural networks (bnns) allow for uncertainty in the predictions to be assessed, different sources of uncertainty are indistinguishable. we present credal bayesian deep learning (cbdl). heuristically, cbdl allows to train an (uncountably) infinite ensemble of bnns, using only finitely many elements. this is possible thanks to prior and likelihood finitely generated credal sets (fgcss), a concept from the imprecise probability literature. intuitively, convex combinations of a finite collection of prior-likelihood pairs are able to represent infinitely many such pairs. after training, cbdl outputs a set of posteriors on the parameters of the neural network. at inference time, such posterior set is used to derive a set of predictive distributions that is in turn utilized to distinguish between aleatoric and epistemic uncertainties, and to quantify them. the predictive set also produces either (i) a collection of outputs enjoying desirable probabilistic guarantees, or (ii) the single output that is deemed the best, that is, the one having the highest predictive lower probability -- another imprecise-probabilistic concept. cbdl is more robust than single bnns to prior and likelihood misspecification, and to distribution shift. we show that cbdl is better at quantifying and disentangling different types of uncertainties than single bnns, ensemble of bnns, and bayesian model averaging. in addition, we apply cbdl to two case studies to demonstrate its downstream tasks capabilities: one, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. we show that cbdl performs better when compared to an ensemble of bnns baseline.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2023-02-19",
"updated": "2024-02-22",
"authors": [
"michele caprio",
"souradeep dutta",
"kuk jin jang",
"vivian lin",
"radoslav ivanov",
"oleg sokolsky",
"insup lee"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2302.09656"
} | "2024-03-15T04:08:18.406723" | {
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} | [] | "algorithm" | "e2271d09-3594-4200-b0f8-d7d460ea5c65" | 1329 | hard |
|
\begin{algorithm}
\caption{Training GANs-based auction features generator}
\begin{algorithmic}[1]
\State $D_{train} \gets$ Initialize training set
\While {$C(fake)>threshold$} \Comment{The critic can be optimized until $C(fake)$ is near $0$. }
\State Randomly select a discrete variable $c$ with equal probability
\State Compute the probability mass function (PMF) of $c$
\State Randomly select a state $i^*$ inherent to $c$ according its PMF
\State Create the conditional vector $cond$ so that $\sum_i cond(i) = 1$ and $cond(i^*)=1$
\For {$batch \in \{1,\dots,N_{batches}\}$} \Comment{Gradient descent with mini-batch}
\State $real \gets d(c_{i^*}=1)\sim D_{train}$ \Comment{Sample batch of real examples respecting the constraint}
\State $z \sim \mathcal{N}(0,1)$ \Comment{Sample noise}
\State $fake \gets \tilde{d} \sim G(z)$ \Comment{Sample fake examples}
\State $real \gets [real]\times 10$ \Comment{Stack input 10 times for Pac configuration}
\State $fake \gets [fake] \times 10$
\State $L^j \gets \big( C(fake_j) - C(real_j)\big) + CE(\tilde{c}, cond)$
\State $L^{batch} \gets L^{batch} + \lambda(||\nabla L^{batch} ||_{2} - 1)^2$ \Comment{Apply gradient penalty}
\State $w_{crit} \gets w_{crit} + Adam(\nabla_{w_{crit}}\frac{1}{m}\sum_i^m L^{batch}(i))$ \Comment{Updating $C$ with Adam}
\If {$batch \bmod k = 0$} \Comment{Synchronicity, depends on $k$}
\State $w_{gen} \gets w_{gen} + Adam(\nabla_{w_{gen}}\frac{1}{m}\sum_i^m -C(G(z)))$ \Comment{Updating $G$ with Adam}
\EndIf
\EndFor
\EndWhile
\end{algorithmic}
\label{alg:ctwgan}
\end{algorithm}
| \begin{algorithm}
\caption{Training GANs-based auction features generator}
\begin{algorithmic}
[1]
\State $D_{train} \gets$ Initialize training set
\While {$C(fake)>threshold$} \Comment{The critic can be optimized until $C(fake)$ is near $0$. }
\State Randomly select a discrete variable $c$ with equal probability
\State Compute the probability mass function (PMF) of $c$
\State Randomly select a state $i^*$ inherent to $c$ according its PMF
\State Create the conditional vector $cond$ so that $\sum_i cond(i) = 1$ and $cond(i^*)=1$
\For {$batch \in \{1,\dots,N_{batches}\}$} \Comment{Gradient descent with mini-batch}
\State $real \gets d(c_{i^*}=1)\sim D_{train}$ \Comment{Sample batch of real examples respecting the constraint}
\State $z \sim \mathcal{N}(0,1)$ \Comment{Sample noise}
\State $fake \gets \tilde{d} \sim G(z)$ \Comment{Sample fake examples}
\State $real \gets [real]\times 10$ \Comment{Stack input 10 times for Pac configuration}
\State $fake \gets [fake] \times 10$
\State $L^j \gets \big( C(fake_j) - C(real_j)\big) + CE(\tilde{c}, cond)$
\State $L^{batch} \gets L^{batch} + \lambda(||\nabla L^{batch} ||_{2} - 1)^2$ \Comment{Apply gradient penalty}
\State $w_{crit} \gets w_{crit} + Adam(\nabla_{w_{crit}}\frac{1}{m}\sum_i^m L^{batch}(i))$ \Comment{Updating $C$ with Adam}
\If {$batch \bmod k = 0$} \Comment{Synchronicity, depends on $k$}
\State $w_{gen} \gets w_{gen} + Adam(\nabla_{w_{gen}}\frac{1}{m}\sum_i^m -C(G(z)))$ \Comment{Updating $G$ with Adam}
\EndIf
\EndFor
\EndWhile
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2207.12255" | "2207.12255.tar.gz" | "2024-02-15" | {
"title": "implementing a hierarchical deep learning approach for simulating multi-level auction data",
"id": "2207.12255",
"abstract": "we present a deep learning solution to address the challenges of simulating realistic synthetic first-price sealed-bid auction data. the complexities encountered in this type of auction data include high-cardinality discrete feature spaces and a multilevel structure arising from multiple bids associated with a single auction instance. our methodology combines deep generative modeling (dgm) with an artificial learner that predicts the conditional bid distribution based on auction characteristics, contributing to advancements in simulation-based research. this approach lays the groundwork for creating realistic auction environments suitable for agent-based learning and modeling applications. our contribution is twofold: we introduce a comprehensive methodology for simulating multilevel discrete auction data, and we underscore the potential of dgm as a powerful instrument for refining simulation techniques and fostering the development of economic models grounded in generative ai.",
"categories": "econ.gn q-fin.ec",
"doi": "",
"created": "2022-07-25",
"updated": "2024-02-15",
"authors": [
"igor sadoune",
"andrea lodi",
"marcelin joanis"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.12255"
} | "2024-03-15T03:57:59.120702" | {
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} | [] | "algorithm" | "f989ce39-7f87-47e1-b412-145869315f0f" | 1537 | hard |
|
\begin{algorithmic}[1]
\Require Bell sample $r \leftarrow P_\rho$.
\If{$\pi_Y(r) = 1$}
\State Declare an error and abort.
\EndIf
\Ensure $r$
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require Bell sample $r \leftarrow P_\rho$.
\If{$\pi_Y(r) = 1$}
\State Declare an error and abort.
\EndIf
\Ensure $r$
\end{algorithmic} | "https://arxiv.org/src/2306.00083" | "2306.00083.tar.gz" | "2024-01-31" | {
"title": "bell sampling from quantum circuits",
"id": "2306.00083",
"abstract": "a central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. in this work, we find a universal model of quantum computation, bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. in bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal bell basis. we show that the bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. in addition to known properties that can be efficiently extracted from bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of t gates in the circuit. with some additional measurements, our algorithm learns a full description of states prepared by circuits with low t-count.",
"categories": "quant-ph cond-mat.quant-gas cs.cc",
"doi": "",
"created": "2023-05-31",
"updated": "2024-01-31",
"authors": [
"dominik hangleiter",
"michael j. gullans"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2306.00083"
} | "2024-03-15T06:26:35.245596" | {
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} | [] | "algorithm" | "64af60f6-fa98-471f-ad09-514444e64eaa" | 159 | easy |
|
\begin{algorithm}[h!]
\caption{MIP-CDA.}
\label{al:mip_cda}
Constants: $\epsilon_{OBJ}=10^{-5}$, $MAXITER=20$\\
\begin{algorithmic}[1]
\State $\omega^{(0)}\leftarrow~\texttt{Relax}()$, $\text{OBJ}^{(0)}\leftarrow \infty$; \hfill (See Algorithm \ref{al:relax})
\State $(\omega^{(1)}, \gamma^{(1)}, \beta^{(1)}, \delta^{(1)})\leftarrow~\texttt{MIP}(\texttt{start}=\omega^{(0)}; \texttt{bestobjstop}=10^{-2})$;
\State $\text{OBJ}^{(1)} \leftarrow M_n(\omega^{(1)}, \gamma^{(1)}, \beta^{(1)}, \delta^{(1)})$;
\State $(\omega^*, \gamma^*, \beta^*, \delta^*) \leftarrow (\omega^{(1)}, \gamma^{(1)}, \beta^{(1)}, \delta^{(1)})$
\For{$k = 2, 3,..., MAXITER$}
\If {$|\text{OBJ}^{(k)} - \text{OBJ}^{(k-1)}| < \epsilon_{OBJ}$}
\State EXIT;
\EndIf
\State $(\omega^{(k)}, \gamma^{(k)})\leftarrow~\texttt{MIP-PROFILE}(\texttt{start}=(\beta^{(k-1)}, \delta^{(k-1)}))$; \hfill (See Section \ref{asec:mip_profile})
\State $\beta^{(k)} \leftarrow {\arg\min}_{\beta}\sum_{i=1}^n(Y_i - Z_i'\beta)^21\{X_i'\omega^{(k)} - \gamma^{(k)}\le 0\}$; \hfill (Least squares)
\State $\delta^{(k)}\leftarrow {\arg\min}_{\delta}\sum_{i=1}^n(Y_i - Z_i'\delta)^21\{X_i'\omega^{(k)} - \gamma^{(k)} > 0\}$; \hfill (Least squares)
\State $\text{OBJ}^{(k)} \leftarrow M_n(\omega^{(k)}, \gamma^{(k)}, \beta^{(k)}, \delta^{(k)})$;
\State $(\omega^*, \gamma^*, \beta^*, \delta^*) \leftarrow (\omega^{(k)}, \gamma^{(k)}, \beta^{(k)}, \delta^{(k)})$
\EndFor % end while loop
\State $\hat \omega, \hat \gamma \leftarrow \texttt{MeanArg}(\omega^*, \gamma^*)$; \hfill (See Algorithm \ref{al:arg})
\State $\check \omega, \check \gamma \leftarrow \texttt{ModeArg}(\omega^*, \gamma^*)$; \hfill (See Algorithm \ref{al:arg})
\State $\hat \beta \leftarrow \check \beta \leftarrow \beta^*$;
\State $\hat \delta \leftarrow \check\delta \leftarrow \delta^*$;
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[h!]
\caption{MIP-CDA.}
Constants: $\epsilon_{OBJ}=10^{-5}$, $MAXITER=20$\\
\begin{algorithmic}
[1]
\State $\omega^{(0)}\leftarrow~\texttt{Relax}()$, $\text{OBJ}^{(0)}\leftarrow \infty$; \hfill (See Algorithm \ref{al:relax})
\State $(\omega^{(1)}, \gamma^{(1)}, \beta^{(1)}, \delta^{(1)})\leftarrow~\texttt{MIP}(\texttt{start}=\omega^{(0)}; \texttt{bestobjstop}=10^{-2})$;
\State $\text{OBJ}^{(1)} \leftarrow M_n(\omega^{(1)}, \gamma^{(1)}, \beta^{(1)}, \delta^{(1)})$;
\State $(\omega^*, \gamma^*, \beta^*, \delta^*) \leftarrow (\omega^{(1)}, \gamma^{(1)}, \beta^{(1)}, \delta^{(1)})$
\For{$k = 2, 3,..., MAXITER$}
\If {$|\text{OBJ}^{(k)} - \text{OBJ}^{(k-1)}| < \epsilon_{OBJ}$}
\State EXIT;
\EndIf
\State $(\omega^{(k)}, \gamma^{(k)})\leftarrow~\texttt{MIP-PROFILE}(\texttt{start}=(\beta^{(k-1)}, \delta^{(k-1)}))$; \hfill (See Section \ref{asec:mip_profile})
\State $\beta^{(k)} \leftarrow {\arg\min}_{\beta}\sum_{i=1}^n(Y_i - Z_i'\beta)^21\{X_i'\omega^{(k)} - \gamma^{(k)}\le 0\}$; \hfill (Least squares)
\State $\delta^{(k)}\leftarrow {\arg\min}_{\delta}\sum_{i=1}^n(Y_i - Z_i'\delta)^21\{X_i'\omega^{(k)} - \gamma^{(k)} > 0\}$; \hfill (Least squares)
\State $\text{OBJ}^{(k)} \leftarrow M_n(\omega^{(k)}, \gamma^{(k)}, \beta^{(k)}, \delta^{(k)})$;
\State $(\omega^*, \gamma^*, \beta^*, \delta^*) \leftarrow (\omega^{(k)}, \gamma^{(k)}, \beta^{(k)}, \delta^{(k)})$
\EndFor % end while loop
\State $\hat \omega, \hat \gamma \leftarrow \texttt{MeanArg}(\omega^*, \gamma^*)$; \hfill (See Algorithm \ref{al:arg})
\State $\check \omega, \check \gamma \leftarrow \texttt{ModeArg}(\omega^*, \gamma^*)$; \hfill (See Algorithm \ref{al:arg})
\State $\hat \beta \leftarrow \check \beta \leftarrow \beta^*$;
\State $\hat \delta \leftarrow \check\delta \leftarrow \delta^*$;
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2206.06140" | "2206.06140.tar.gz" | "2024-01-13" | {
"title": "inference for change-plane regression",
"id": "2206.06140",
"abstract": "a key challenge in analyzing the behavior of change-plane estimators is that the objective function has multiple minimizers. two estimators are proposed to deal with this non-uniqueness. for each estimator, an n-rate of convergence is established, and the limiting distribution is derived. based on these results, we provide a parametric bootstrap procedure for inference. the validity of our theoretical results and the finite sample performance of the bootstrap are demonstrated through simulation experiments. we illustrate the proposed methods to latent subgroup identification in precision medicine using the actg175 aids study data.",
"categories": "math.st stat.th",
"doi": "",
"created": "2022-06-13",
"updated": "2024-01-13",
"authors": [
"chaeryon kang",
"hunyong cho",
"rui song",
"moulinath banerjee",
"eric b. laber",
"michael r. kosorok"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.06140"
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} | {
"num_done": {
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"algorithm": 3
}
} | {
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} | [] | "algorithm" | "de619293-f51b-435f-bbaf-47e448c7aaa3" | 1819 | hard |
|
\begin{algorithmic}[1]
\State \textbf{Input}: matrix observations $\{\mathbf{X}_t\}_{t=1}^T$, factor numbers $k_1$ and $k_2$.
\State Estimate loading matrices by equations \eqref{estimator_R} and \eqref{estimator_C}.
\State Estimate factor matrices and the signal part by equations \eqref{factormatrix_RaDFaM} and \eqref{signal_RaDFaM} for $t\in[T]$.
\State \textbf{Output}: $\widehat{\mathbf{R}}$, $\widehat{\mathbf{C}}$, $\{\widehat{\mathbf{Z}}_t\}_{t=1}^T$,
$\{\widehat{\mathbf{F}}_t\}_{t=1}^T$, $\{\widehat{\mathbf{E}}_t\}_{t=1}^T$, and $\{\widehat{\mathbf{S}}_t\}_{t=1}^T$.
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input}: matrix observations $\{\mathbf{X}_t\}_{t=1}^T$, factor numbers $k_1$ and $k_2$.
\State Estimate loading matrices by equations \eqref{estimator_R} and \eqref{estimator_C}.
\State Estimate factor matrices and the signal part by equations \eqref{factormatrix_RaDFaM} and \eqref{signal_RaDFaM} for $t\in[T]$.
\State \textbf{Output}: $\widehat{\mathbf{R}}$, $\widehat{\mathbf{C}}$, $\{\widehat{\mathbf{Z}}_t\}_{t=1}^T$,
$\{\widehat{\mathbf{F}}_t\}_{t=1}^T$, $\{\widehat{\mathbf{E}}_t\}_{t=1}^T$, and $\{\widehat{\mathbf{S}}_t\}_{t=1}^T$.
\end{algorithmic} | "https://arxiv.org/src/2209.14846" | "2209.14846.tar.gz" | "2024-02-12" | {
"title": "modeling and learning on high-dimensional matrix-variate sequences",
"id": "2209.14846",
"abstract": "we propose a new matrix factor model, named radfam, which is strictly derived based on the general rank decomposition and assumes a structure of a high-dimensional vector factor model for each basis vector. radfam contributes a novel class of low-rank latent structure that makes tradeoff between signal intensity and dimension reduction from the perspective of tensor subspace. based on the intrinsic separable covariance structure of radfam, for a collection of matrix-valued observations, we derive a new class of pca variants for estimating loading matrices, and sequentially the latent factor matrices. the peak signal-to-noise ratio of radfam is proved to be superior in the category of pca-type estimations. we also establish the asymptotic theory including the consistency, convergence rates, and asymptotic distributions for components in the signal part. numerically, we demonstrate the performance of radfam in applications such as matrix reconstruction, supervised learning, and clustering, on uncorrelated and correlated data, respectively.",
"categories": "stat.me",
"doi": "",
"created": "2022-09-29",
"updated": "2024-02-12",
"authors": [
"xu zhang",
"catherine c. liu",
"jianhua guo",
"k. c. yuen",
"a. h. welsh"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2209.14846"
} | "2024-03-15T05:49:17.008547" | {
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} | {
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} | [] | "algorithm" | "d853d5f8-1195-4891-871c-ae4f9fc20530" | 597 | easy |
|
\begin{algorithmic}
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Retrieve the values of $P_{u,t}$}
\State $P_{u,t}\leftarrow\textrm{{\tt Power.GetValue}}(t)$
\EndFor
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Initial conditions on the state variables}
\If{$P_{u,t} > \textrm{{\tt MinimumPower.GetValue}}(t)$}
\State $S_{u,t}^{OFF} \leftarrow 0$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\If{$P_{u,t} < P_{u,t-1}$}\Comment{Exact initialization required only if the FLAT state is defined.}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 1$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} > P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 1$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} = P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 1$
\EndIf
\ElsIf{$P_{u,t} > 0$}\Comment{Reconstruct the startups and shutdowns}
\If{$P_{u,t} < P_{u,t-1}$}
\State $S_{t}^{STOP} \leftarrow 1$
\State $S_{t}^{START} \leftarrow 0$
\Else
\State $S_{t}^{STOP} \leftarrow 0$
\State $S_{t}^{START} \leftarrow 1$
\EndIf
\Else\Comment{Final possibility: the unit is OFF.}
\State $S_{u,t}^{OFF} \leftarrow 1$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\EndIf
\EndFor
\end{algorithmic}
| \begin{algorithmic}
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Retrieve the values of $P_{u,t}$}
\State $P_{u,t}\leftarrow\textrm{{\tt Power.GetValue}}(t)$
\EndFor
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Initial conditions on the state variables}
\If{$P_{u,t} > \textrm{{\tt MinimumPower.GetValue}}(t)$}
\State $S_{u,t}^{OFF} \leftarrow 0$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\If{$P_{u,t} < P_{u,t-1}$}\Comment{Exact initialization required only if the FLAT state is defined.}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 1$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} > P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 1$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} = P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 1$
\EndIf
\ElsIf{$P_{u,t} > 0$}\Comment{Reconstruct the startups and shutdowns}
\If{$P_{u,t} < P_{u,t-1}$}
\State $S_{t}^{STOP} \leftarrow 1$
\State $S_{t}^{START} \leftarrow 0$
\Else
\State $S_{t}^{STOP} \leftarrow 0$
\State $S_{t}^{START} \leftarrow 1$
\EndIf
\Else\Comment{Final possibility: the unit is OFF.}
\State $S_{u,t}^{OFF} \leftarrow 1$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\EndIf
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2402.12848" | "2402.12848.tar.gz" | "2024-02-20" | {
"title": "atlas: a model of short-term european electricity market processes under uncertainty",
"id": "2402.12848",
"abstract": "the atlas model simulates the various stages of the electricity market chain in europe, including the formulation of offers by different market actors, the coupling of european markets, strategic optimization of production portfolios and, finally, real-time system balancing processes. atlas was designed to simulate the various electricity markets and processes that occur from the day ahead timeframe to real-time with a high level of detail. its main aim is to capture impacts from imperfect actor coordination, evolving forecast errors and a high-level of technical constraints--both regarding different production units and the different market constraints.",
"categories": "econ.gn math.oc q-fin.ec",
"doi": "",
"created": "2024-02-20",
"updated": "",
"authors": [
"emily little",
"florent cogen",
"quentin bustarret",
"virginie dussartre",
"maxime l\u00e2asri",
"gabriel kasmi",
"marie girod",
"frederic bienvenu",
"maxime fortin",
"jean-yves bourmaud"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.12848"
} | "2024-03-15T03:29:36.738175" | {
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} | [] | "algorithm" | "56d94178-c64a-400a-8ad1-dc94af078bcd" | 1526 | hard |
|
\begin{algorithm}[H]
\caption{Basic elastic formulation slice division process (negative balancing needs)}\label{alg:elastic_slice_division_neg}
\begin{algorithmic}
\State \textbf{\textit{Initialization of the set of time steps}}
\State $T_{div} \gets {t \in T_{m} \mkern9mu | \mkern9mu bn_{t} < 0}$\\
\State \textbf{\textit{Initialization of the first slice $i = 1$}}
\State $V_{1} \gets \max(-V^{s}, \max\limits_{t \in T_{div}} bn_{t})$\\
\State \textbf{\textit{Recursion}}
\For{$i > 1$}
\While{$\mkern9mu \sum\limits_{1 \leq j < i} (V_{j}) > \min\limits_{t \in T_{div}} bn_{t}$}
\State $V_{i} \gets \max(-V^{s}, \max\limits_{t \in T_{div}} (bn_{t} - \sum\limits_{1 \leq j < i} (V_{j})))$\Comment{Compute the maximum size of $V_{i}$}\\
\For{$t \in T_{div}$}
\State $q_{t,i} \gets |V_{i}|$\Comment{Extract the order quantity for relevant time steps}
\State $\sigma_{t,i} \gets 1$\Comment{Set the order direction}
\If{$bn_{t} - \sum\limits_{1 \leq j \leq i} (V_{j}) = 0$}\Comment{Remove now "empty" time steps from $T_{div}$}
\State $T_{div} \gets T_{div} - \{t\}$
\EndIf
\EndFor
\State $i \gets i+1$
\EndWhile
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Basic elastic formulation slice division process (negative balancing needs)} \begin{algorithmic}
\State \textbf{\textit{Initialization of the set of time steps}}
\State $T_{div} \gets {t \in T_{m} \mkern9mu | \mkern9mu bn_{t} < 0}$\\
\State \textbf{\textit{Initialization of the first slice $i = 1$}}
\State $V_{1} \gets \max(-V^{s}, \max\limits_{t \in T_{div}} bn_{t})$\\
\State \textbf{\textit{Recursion}}
\For{$i > 1$}
\While{$\mkern9mu \sum\limits_{1 \leq j < i} (V_{j}) > \min\limits_{t \in T_{div}} bn_{t}$}
\State $V_{i} \gets \max(-V^{s}, \max\limits_{t \in T_{div}} (bn_{t} - \sum\limits_{1 \leq j < i} (V_{j})))$\Comment{Compute the maximum size of $V_{i}$}\\
\For{$t \in T_{div}$}
\State $q_{t,i} \gets |V_{i}|$\Comment{Extract the order quantity for relevant time steps}
\State $\sigma_{t,i} \gets 1$\Comment{Set the order direction}
\If{$bn_{t} - \sum\limits_{1 \leq j \leq i} (V_{j}) = 0$}\Comment{Remove now "empty" time steps from $T_{div}$}
\State $T_{div} \gets T_{div} - \{t\}$
\EndIf
\EndFor
\State $i \gets i+1$
\EndWhile
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.12859" | "2402.12859.tar.gz" | "2024-02-20" | {
"title": "atlas: a model of short-term european electricity market processes under uncertainty -- balancing modules",
"id": "2402.12859",
"abstract": "the atlas model simulates the various stages of the electricity market chain in europe, including the formulation of offers by different market actors, the coupling of european markets, strategic optimization of production portfolios and, finally, real-time system balancing processes. atlas was designed to simulate the various electricity markets and processes that occur from the day ahead timeframe to real-time with a high level of detail. its main aim is to capture impacts from imperfect actor coordination, evolving forecast errors and a high-level of technical constraints -- both regarding different production units and the different market constraints. this working paper describes the simulated balancing processes in detail and is the second part of the atlas documentation.",
"categories": "econ.gn math.oc q-fin.ec",
"doi": "",
"created": "2024-02-20",
"updated": "",
"authors": [
"florent cogen",
"emily little",
"virginie dussartre",
"quentin bustarret"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.12859"
} | "2024-03-15T03:21:13.620616" | {
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} | [] | "algorithm" | "9a709d7b-4c26-44c4-9cab-8d4c9b748615" | 1115 | medium |
|
\begin{algorithmic}
\State 1. Considering the dataset of all applicants to both programs, randomly split the dataset into train and test with equal probability at the applicant level, denote the resulting sets as $I^{train} = \left\{1,..,\mathcal{I}^{train}\right\}$ and $I^{test}= \left\{1,..,\mathcal{I}^{test}\right\}$.
\State 2. In the training dataset, estimate outcome model using cross-validation: $\mu_{train}$
\State 3. In the test set, construct predicted treatment effects using predictions from model $\mu_{train}$. Obtain $\tau^{Op,train}_{i,t} = E[\hat{Y}(p)_{train} - \hat{Y}(O)_{train}|X=x_{i,t} , i \in I^{test}]$, where $\hat{Y}(p)_{train}$ is the predicted outcome under program $p$ constructed using $\mu_{train}$ and $\hat{Y}(O)_{train}$ is the predicted outcome under \emph{Out of Dare IT} and $t \in \left\{1,...,15\right\}$ denotes months. Compute mean treatment effects per user as: $\tau^{Op,train}_{i} = 1/t \times \sum_{t=1}^{15}\tau^{Op,train}_{i,t}$,
\State 4. Assign treatment to maximize treatment effects subject to capacity constraint. Let $Q^{p}$ be the capacity limit of program $p$ and $z_{ip}$ an indicator variable taking the value of one when applicant $i$ is assigned to program $p$ and zero otherwise. We solve the following constrained optimization problem:
\[
\max_{z_{ip}}\sum_{i=1}^{I}\sum_{p=1}^{P}z_{ip}\tau_{i}^{Op,train} \text{ s.t. }\sum_{i=1}^{I}z_{ip} \leq Q^{p} \forall_{p} \text{ \& }\sum_{i=p}^{P}z_{ip} = 1\forall_{i \in I^{test}}.
\] The first constraint ensures that the capacity constraints are not violated. The second one is that every applicant is assigned to one program. There is no capacity limit on being \emph{Out of Dare IT}. We use \emph{LP Solve} algorithm to solve the problem. We obtain optimal allocation $\mathcal{A}_{X,Q}^{*} = \left\{a_{i}^{*},...,a_{\mathcal{I}^{test}}^{*}\right\}$,
\State 5. Using the test set, estimate new outcome and propensity models using cross-fitting and obtain predictions: $\hat{\mu}_{i,k}$ and $\hat{e}_{i,k}$ for all $i \in I^{test}$. See Appendix \ref{cross_fit_appendix} for details of the cross-fitting procedure. Obtain $\hat{Y}_{i,k}(a^{*})$ the AIPW estimates of the predicted outcomes using cross-fitted models trained in the test set,
\State 6. Obtain $\hat{V}_{X,Q}^{*} = \frac{1}{|I^{test}|}\times \sum_{i=1}^{\mathcal{I}^{test}}\hat{Y}_{i,k}(a^{*})$ as the mean of predicted outcomes under the allocation $\mathcal{A}_{X,Q}^{*}$. Estimate standard errors clustered at the applicant level: $\sigma_{X,Q}^{*}$. \Comment \\
\Return{} $(\mathcal{A}_{X,Q}^{*},\hat{V}_{X,Q}^{*},\sigma_{X,Q}^{*},\hat{Y}_{1,k}(a^{*}),...,\hat{Y}_{\mathcal{I}^{test},k}(a^{*}) )$
\end{algorithmic}
| \begin{algorithmic}
\State 1. Considering the dataset of all applicants to both programs, randomly split the dataset into train and test with equal probability at the applicant level, denote the resulting sets as $I^{train} = \left\{1,..,\mathcal{I}^{train}\right\}$ and $I^{test}= \left\{1,..,\mathcal{I}^{test}\right\}$.
\State 2. In the training dataset, estimate outcome model using cross-validation: $\mu_{train}$
\State 3. In the test set, construct predicted treatment effects using predictions from model $\mu_{train}$. Obtain $\tau^{Op,train}_{i,t} = E[\hat{Y}(p)_{train} - \hat{Y}(O)_{train}|X=x_{i,t} , i \in I^{test}]$, where $\hat{Y}(p)_{train}$ is the predicted outcome under program $p$ constructed using $\mu_{train}$ and $\hat{Y}(O)_{train}$ is the predicted outcome under \emph{Out of Dare IT} and $t \in \left\{1,...,15\right\}$ denotes months. Compute mean treatment effects per user as: $\tau^{Op,train}_{i} = 1/t \times \sum_{t=1}^{15}\tau^{Op,train}_{i,t}$,
\State 4. Assign treatment to maximize treatment effects subject to capacity constraint. Let $Q^{p}$ be the capacity limit of program $p$ and $z_{ip}$ an indicator variable taking the value of one when applicant $i$ is assigned to program $p$ and zero otherwise. We solve the following constrained optimization problem:
\[
\max_{z_{ip}}\sum_{i=1}^{I}\sum_{p=1}^{P}z_{ip}\tau_{i}^{Op,train} \text{ s.t. }\sum_{i=1}^{I}z_{ip} \leq Q^{p} \forall_{p} \text{ \& }\sum_{i=p}^{P}z_{ip} = 1\forall_{i \in I^{test}}.
\] The first constraint ensures that the capacity constraints are not violated. The second one is that every applicant is assigned to one program. There is no capacity limit on being \emph{Out of Dare IT}. We use \emph{LP Solve} algorithm to solve the problem. We obtain optimal allocation $\mathcal{A}_{X,Q}^{*} = \left\{a_{i}^{*},...,a_{\mathcal{I}^{test}}^{*}\right\}$,
\State 5. Using the test set, estimate new outcome and propensity models using cross-fitting and obtain predictions: $\hat{\mu}_{i,k}$ and $\hat{e}_{i,k}$ for all $i \in I^{test}$. See Appendix \ref{cross_fit_appendix} for details of the cross-fitting procedure. Obtain $\hat{Y}_{i,k}(a^{*})$ the AIPW estimates of the predicted outcomes using cross-fitted models trained in the test set,
\State 6. Obtain $\hat{V}_{X,Q}^{*} = \frac{1}{|I^{test}|}\times \sum_{i=1}^{\mathcal{I}^{test}}\hat{Y}_{i,k}(a^{*})$ as the mean of predicted outcomes under the allocation $\mathcal{A}_{X,Q}^{*}$. Estimate standard errors clustered at the applicant level: $\sigma_{X,Q}^{*}$. \Comment \\
\Return{} $(\mathcal{A}_{X,Q}^{*},\hat{V}_{X,Q}^{*},\sigma_{X,Q}^{*},\hat{Y}_{1,k}(a^{*}),...,\hat{Y}_{\mathcal{I}^{test},k}(a^{*}) )$
\end{algorithmic} | "https://arxiv.org/src/2211.09968" | "2211.09968.tar.gz" | "2024-01-03" | {
"title": "effective and scalable programs to facilitate labor market transitions for women in technology",
"id": "2211.09968",
"abstract": "we describe the design, implementation, and evaluation of a low-cost (approximately $15 per person) and scalable program, called challenges, aimed at aiding women in poland transition to technology-sector jobs. this program helps participants develop portfolios demonstrating job-relevant competencies. we conduct two independent evaluations, one of the challenges program and the other of a traditional mentoring program -- mentoring -- where experienced tech professionals work individually with mentees to support them in their job search. exploiting the fact that both programs were oversubscribed, we randomized admissions and measured their impact on the probability of finding a job in the technology sector. we estimate that mentoring increases the probability of finding a technology job within four months from 29% to 42% and challenges from 20% to 29%, and the treatment effects do not attenuate over 12 months. since both programs are capacity constrained in practice (only 28% of applicants can be accommodated), we evaluate the effectiveness of several alternative prioritization rules based on applicant characteristics. we find that a policy that selects applicants based on their predicted treatment effects increases the average treatment effect across the two programs to 22 percentage points. we further analyze how alternative prioritization rules compare to the selection that mentors used. we find that mentors selected applicants who were more likely to get a tech job even without participating in the program, and the treatment effect for applicants with similar characteristics to those selected by mentors is about half of the effect attainable when participants are prioritized optimally.",
"categories": "econ.gn q-fin.ec",
"doi": "",
"created": "2022-11-17",
"updated": "2024-01-03",
"authors": [
"susan athey",
"emil palikot"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.09968"
} | "2024-03-15T06:43:58.018752" | {
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} | [] | "algorithm" | "3b37cbbc-c141-49d2-9c5f-1c13033cb6a7" | 2692 | hard |
|
\begin{algorithmic}
\State Initialize \(k=1, \mathbf{w}\sim Uniform(|\Phi|)\)
\State Set \(\sigma=0, J_{\text{prev}} = J(\mathbf{w},\sigma)\)
\While{\(k<k_{max}\)}
\State Compute gradient \(\nabla_\mathbf{w} J(\mathbf{w},\sigma)\)
\If{\(\left\|\nabla_\mathbf{w} J(\mathbf{w},\sigma) - \frac{\nabla_\mathbf{w} J(\mathbf{w},\sigma)^\top \mathbf{w}}{\|\mathbf{w}\|^2} \mathbf{w}\right\| < \beta\)}
\State terminate with \(\mathbf{w}\).
\EndIf
\State \(\overline{\mathbf{w}} = \text{Proj}_{L_2}(\mathbf{w} - \alpha \nabla_\mathbf{w} J(\mathbf{w},\sigma))\)
\If{\(J(\overline{\mathbf{w}}, \sigma) > J_{\text{prev}}\)}
\State \(\sigma \gets \sigma + \frac{1}{L}\), continue.
\Else
\State \(\mathbf{w}\gets \overline{\mathbf{w}}\)
\State \(J_{\text{prev}} = J(\mathbf{w},\sigma)\)
\EndIf
\State \(k\gets k+1\)
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
\State Initialize \(k=1, \mathbf{w}\sim Uniform(|\Phi|)\)
\State Set \(\sigma=0, J_{\text{prev}} = J(\mathbf{w},\sigma)\)
\While{\(k<k_{max}\)}
\State Compute gradient \(\nabla_\mathbf{w} J(\mathbf{w},\sigma)\)
\If{\(\left\|\nabla_\mathbf{w} J(\mathbf{w},\sigma) - \frac{\nabla_\mathbf{w} J(\mathbf{w},\sigma)^\top \mathbf{w}}{\|\mathbf{w}\|^2} \mathbf{w}\right\| < \beta\)}
\State terminate with \(\mathbf{w}\).
\EndIf
\State \(\overline{\mathbf{w}} = \text{Proj}_{L_2}(\mathbf{w} - \alpha \nabla_\mathbf{w} J(\mathbf{w},\sigma))\)
\If{\(J(\overline{\mathbf{w}}, \sigma) > J_{\text{prev}}\)}
\State \(\sigma \gets \sigma + \frac{1}{L}\), continue.
\Else
\State \(\mathbf{w}\gets \overline{\mathbf{w}}\)
\State \(J_{\text{prev}} = J(\mathbf{w},\sigma)\)
\EndIf
\State \(k\gets k+1\)
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2207.06392" | "2207.06392.tar.gz" | "2024-01-25" | {
"title": "relationship design for socially-aware behavior in static games",
"id": "2207.06392",
"abstract": "autonomous agents can adopt socially-aware behaviors to reduce social costs, mimicking the way animals interact in nature and humans in society. we present a new approach to model socially-aware decision-making that includes two key elements: bounded rationality and inter-agent relationships. we capture the interagent relationships by introducing a novel model called a relationship game and encode agents' bounded rationality using quantal response equilibria. for each relationship game, we define a social cost function and formulate a mechanism design problem to optimize weights for relationships that minimize social cost at the equilibrium. we address the multiplicity of equilibria by presenting the problem in two forms: min-max and min-min, aimed respectively at minimization of the highest and lowest social costs in the equilibria. we compute the quantal response equilibrium by solving a least-squares problem defined with its karush-kuhn-tucker conditions, and propose two projected gradient descent algorithms to solve the mechanism design problems. numerical results, including two-lane congestion and congestion with an ambulance, confirm that these algorithms consistently reach the equilibrium with the intended social costs.",
"categories": "cs.ma cs.sy eess.sy",
"doi": "",
"created": "2022-07-13",
"updated": "2024-01-25",
"authors": [
"shenghui chen",
"yigit e. bayiz",
"david fridovich-keil",
"ufuk topcu"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.06392"
} | "2024-03-15T08:38:27.674079" | {
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} | [] | "algorithm" | "9176bd5b-eb5b-4137-a59e-c29b8db642a9" | 830 | medium |
|
\begin{algorithm}[!h]
\caption{HKSL Learning Loop}\label{alg:hksl}
\begin{algorithmic}[1]
\Require trajectory $\tau$
\For{layer $i$ in HKSL (begin with the lowest layer)}
\For{layer $j$ in HKSL (begin with the highest layer)}
\If{$i == j$}
\State break loop
\EndIf
\State Embed first observation $o$ in $\tau$ using layer $j$'s encoder
\If{layer $j$ is the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model and actions from $\tau$
\State Store the prediction
\EndFor
\Else{ layer $j$ is not the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Store the prediction
\EndFor
\EndIf
\EndFor
\State Embed first observation $o$ in $\tau$ using layer $i$'s encoder
\For{step layer $i$ can take in $\tau$}
\State Compute forward-step using layer $i$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Project the forward model's output with layer $i$'s nonlinear projection
\State Compute loss per Equation~\ref{eqn:hksl-loss}
\EndFor
\State Update layer $i$'s weights
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[!h]
\caption{HKSL Learning Loop}\begin{algorithmic}
[1]
\Require trajectory $\tau$
\For{layer $i$ in HKSL (begin with the lowest layer)}
\For{layer $j$ in HKSL (begin with the highest layer)}
\If{$i == j$}
\State break loop
\EndIf
\State Embed first observation $o$ in $\tau$ using layer $j$'s encoder
\If{layer $j$ is the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model and actions from $\tau$
\State Store the prediction
\EndFor
\Else{ layer $j$ is not the top layer}
\For{step layer $j$ can take in $\tau$}
\State Compute forward-step using layer $j$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Store the prediction
\EndFor
\EndIf
\EndFor
\State Embed first observation $o$ in $\tau$ using layer $i$'s encoder
\For{step layer $i$ can take in $\tau$}
\State Compute forward-step using layer $i$'s forward model, actions from $\tau$, and output from communication manager using the stored rollout from above level
\State Project the forward model's output with layer $i$'s nonlinear projection
\State Compute loss per Equation~\ref{eqn:hksl-loss}
\EndFor
\State Update layer $i$'s weights
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2206.11396" | "2206.11396.tar.gz" | "2024-01-29" | {
"title": "multi-horizon representations with hierarchical forward models for reinforcement learning",
"id": "2206.11396",
"abstract": "learning control from pixels is difficult for reinforcement learning (rl) agents because representation learning and policy learning are intertwined. previous approaches remedy this issue with auxiliary representation learning tasks, but they either do not consider the temporal aspect of the problem or only consider single-step transitions, which may cause learning inefficiencies if important environmental changes take many steps to manifest. we propose hierarchical $k$-step latent (hksl), an auxiliary task that learns multiple representations via a hierarchy of forward models that learn to communicate and an ensemble of $n$-step critics that all operate at varying magnitudes of step skipping. we evaluate hksl in a suite of 30 robotic control tasks with and without distractors and a task of our creation. we find that hksl either converges to higher or optimal episodic returns more quickly than several alternative representation learning approaches. furthermore, we find that hksl's representations capture task-relevant details accurately across timescales (even in the presence of distractors) and that communication channels between hierarchy levels organize information based on both sides of the communication process, both of which improve sample efficiency.",
"categories": "cs.lg",
"doi": "",
"created": "2022-06-22",
"updated": "2024-01-29",
"authors": [
"trevor mcinroe",
"lukas sch\u00e4fer",
"stefano v. albrecht"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.11396"
} | "2024-03-15T08:37:32.877079" | {
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} | [] | "algorithm" | "1eb15f76-7aa4-4b51-a942-c42ee02d3f72" | 1294 | hard |
|
\begin{algorithmic}
\Require adjacency matrix $e(j,k)$, $j, k \in X$ and $o\in B$
\Ensure $p(d,j) \in \{0, 1\}$, $d = 1,\dots, n - 1$, $j \in X \setminus \{o\}$, satisfies (P)
\ForAll{$j \in X \setminus \{o\}$}
\If{$e(o,j)=1$}
\State $p(1,j) \gets 1$
\Else
\State $p(1,j) \gets 0$
\EndIf
\EndFor
\For{$d = 2,\dots,n - 1$}
\ForAll{$j \in X \setminus \{o\}$}
\ForAll{$k \in X \setminus \{o,j\}$}
\If{$p(d-1, k) = 1$ and $e(k, j) = 1$}
\State $a(k) \gets 1$
\Else
\State $a(k) \gets 0$
\EndIf
\EndFor
\If{$p(d-1,j) = 1$ or $a(k) = 1$ for some $k \in X \setminus \{o,j\}$}
\State $p(d,j) \gets 1$
\Else
\State $p(d,j) \gets 0$
\EndIf
\EndFor
\EndFor
\end{algorithmic}
| \begin{algorithmic}
\Require adjacency matrix $e(j,k)$, $j, k \in X$ and $o\in B$
\Ensure $p(d,j) \in \{0, 1\}$, $d = 1,\dots, n - 1$, $j \in X \setminus \{o\}$, satisfies (P)
\ForAll{$j \in X \setminus \{o\}$}
\If{$e(o,j)=1$}
\State $p(1,j) \gets 1$
\Else
\State $p(1,j) \gets 0$
\EndIf
\EndFor
\For{$d = 2,\dots,n - 1$}
\ForAll{$j \in X \setminus \{o\}$}
\ForAll{$k \in X \setminus \{o,j\}$}
\If{$p(d-1, k) = 1$ and $e(k, j) = 1$}
\State $a(k) \gets 1$
\Else
\State $a(k) \gets 0$
\EndIf
\EndFor
\If{$p(d-1,j) = 1$ or $a(k) = 1$ for some $k \in X \setminus \{o,j\}$}
\State $p(d,j) \gets 1$
\Else
\State $p(d,j) \gets 0$
\EndIf
\EndFor
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2306.05253" | "2306.05253.tar.gz" | "2024-02-12" | {
"title": "quantum computing algorithms for inverse problems on graphs and an np-complete inverse problem",
"id": "2306.05253",
"abstract": "we consider an inverse problem for a finite graph $(x,e)$ where we are given a subset of vertices $b\\subset x$ and the distances $d_{(x,e)}(b_1,b_2)$ of all vertices $b_1,b_2\\in b$. the distance of points $x_1,x_2\\in x$ is defined as the minimal number of edges needed to connect two vertices, so all edges have length 1. the inverse problem is a discrete version of the boundary rigidity problem in riemannian geometry or the inverse travel time problem in geophysics. we will show that this problem has unique solution under certain conditions and develop quantum computing methods to solve it. we prove the following uniqueness result: when $(x,e)$ is a tree and $b$ is the set of leaves of the tree, the graph $(x,e)$ can be uniquely determined in the class of all graphs having a fixed number of vertices. we present a quantum computing algorithm which produces a graph $(x,e)$, or one of those, which has a given number of vertices and the required distances between vertices in $b$. to this end we develop an algorithm that takes in a qubit representation of a graph and combine it with grover's search algorithm. the algorithm can be implemented using only $o(|x|^2)$ qubits, the same order as the number of elements in the adjacency matrix of $(x,e)$. it also has a quadratic improvement in computational cost compared to standard classical algorithms. finally, we consider applications in theory of computation, and show that a slight modification of the above inverse problem is np-complete: all np-problems can be reduced to a discrete inverse problem we consider.",
"categories": "math.co cs.cc quant-ph",
"doi": "",
"created": "2023-06-08",
"updated": "2024-02-12",
"authors": [
"joonas ilmavirta",
"matti lassas",
"jinpeng lu",
"lauri oksanen",
"lauri ylinen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2306.05253"
} | "2024-03-15T05:16:33.731462" | {
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}
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} | [] | "algorithm" | "5ee302ce-de10-47e1-910c-e2887f6fbafd" | 663 | easy |
|
\begin{algorithm}
\caption{Definite Not Defectives (DND) \cite{kautz1964nonrandom,chen2008survey, chan2011non,aldridge2014group}}\label{alg:cap_coma}
\hspace*{\algorithmicindent} \textbf{Input: $\mathbf{X}, Y$} \\
\hspace*{\algorithmicindent} \textbf{Output: $\mathcal{P}^{(DND)}$}
\begin{algorithmic}[1]
\State $\mathcal{P}^{(DND)} \gets \left\{ 1,...,N \right\}$
\For{$i$ s.t. $\mathbf{Y}_i=0$}
\For{$j$ s.t. $\mathbf{X}_{i,j}=1$}
$\mathcal{P}^{(DND)} \gets \mathcal{P}^{(DND)} \setminus \{j\}$
\EndFor
\EndFor
\State \Return $\mathcal{P}^{(DND)}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Definite Not Defectives (DND) \cite{kautz1964nonrandom,chen2008survey, chan2011non,aldridge2014group}}\hspace*{\algorithmicindent} \textbf{Input: $\mathbf{X}, Y$} \\
\hspace*{\algorithmicindent} \textbf{Output: $\mathcal{P}^{(DND)}$}
\begin{algorithmic}
[1]
\State $\mathcal{P}^{(DND)} \gets \left\{ 1,...,N \right\}$
\For{$i$ s.t. $\mathbf{Y}_i=0$}
\For{$j$ s.t. $\mathbf{X}_{i,j}=1$}
$\mathcal{P}^{(DND)} \gets \mathcal{P}^{(DND)} \setminus \{j\}$
\EndFor
\EndFor
\State \Return $\mathcal{P}^{(DND)}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.10018" | "2402.10018.tar.gz" | "2024-02-15" | {
"title": "multi-stage algorithm for group testing with prior statistics",
"id": "2402.10018",
"abstract": "in this paper, we propose an efficient multi-stage algorithm for non-adaptive group testing (gt) with general correlated prior statistics. the proposed solution can be applied to any correlated statistical prior represented in trellis, e.g., finite state machines and markov processes. we introduce a variation of list viterbi algorithm (lva) to enable accurate recovery using much fewer tests than objectives, which efficiently gains from the correlated prior statistics structure. our numerical results demonstrate that the proposed multi-stage gt (msgt) algorithm can obtain the optimal maximum a posteriori (map) performance with feasible complexity in practical regimes, such as with covid-19 and sparse signal recovery applications, and reduce in the scenarios tested the number of pooled tests by at least $25\\%$ compared to existing classical low complexity gt algorithms. moreover, we analytically characterize the complexity of the proposed msgt algorithm that guarantees its efficiency.",
"categories": "cs.it math.it q-bio.qm stat.ap",
"doi": "",
"created": "2024-02-15",
"updated": "",
"authors": [
"ayelet c. portnoy",
"alejandro cohen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.10018"
} | "2024-03-15T04:32:28.811580" | {
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} | [] | "algorithm" | "b0e9e600-a456-4cdf-ad05-aa1d68e0d505" | 563 | easy |
|
\begin{algorithmic}[1]
\State{\textbf{Input:} set of arms $\mathcal{I}$, horizon length $n_{Q}$, $P$-data $\mathcal{D}^{P}$.}
\For{$s \in \mathcal{S}$}
\State{Initialize the policy $\widetilde{\pi}(s)$ by Procedure~\ref{alg:EA-TL-tabular}$\big(s,\mathcal{I},\mathcal{D}^{P} \big)$.}
\State{Initialize $N(s)\gets0$.}
\Comment{initialize time for policy $\widetilde{\pi}(s)$}
\EndFor
\For{$t=1,\dots,n_{Q}$}
\State{Draw a sample $X_{t}^{Q} \sim Q_{X}$.}
\State{Denote state $s = X_{t}^{Q}$.}
\State{Set $N(s)\gets N(s)+1$.}
\Comment{update times $X_{t}^{Q} = s$}
\State{Set $\pi_{t}\gets\widetilde{\pi}_{N(s)}(s)$.}
\Comment{choose arm by policy $\widetilde{\pi}(s)$}
\EndFor
\State{\textbf{Output:} policy $\{\pi_{t}\}_{t\geq1}$.}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State{\textbf{Input:} set of arms $\mathcal{I}$, horizon length $n_{Q}$, $P$-data $\mathcal{D}^{P}$.}
\For{$s \in \mathcal{S}$}
\State{Initialize the policy $\widetilde{\pi}(s)$ by Procedure~\ref{alg:EA-TL-tabular}$\big(s,\mathcal{I},\mathcal{D}^{P} \big)$.}
\State{Initialize $N(s)\gets0$.}
\Comment{initialize time for policy $\widetilde{\pi}(s)$}
\EndFor
\For{$t=1,\dots,n_{Q}$}
\State{Draw a sample $X_{t}^{Q} \sim Q_{X}$.}
\State{Denote state $s = X_{t}^{Q}$.}
\State{Set $N(s)\gets N(s)+1$.}
\Comment{update times $X_{t}^{Q} = s$}
\State{Set $\pi_{t}\gets\widetilde{\pi}_{N(s)}(s)$.}
\Comment{choose arm by policy $\widetilde{\pi}(s)$}
\EndFor
\State{\textbf{Output:} policy $\{\pi_{t}\}_{t\geq1}$.}
\end{algorithmic} | "https://arxiv.org/src/2211.12612" | "2211.12612.tar.gz" | "2024-01-24" | {
"title": "transfer learning for contextual multi-armed bandits",
"id": "2211.12612",
"abstract": "motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected on source bandits before the start of the target bandit learning. the minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. the results quantify the contribution of the data from the source domains for learning in the target domain in the context of nonparametric contextual multi-armed bandits. in view of the general impossibility of adaptation to unknown smoothness, we develop a data-driven algorithm that achieves near-optimal statistical guarantees (up to a logarithmic factor) while automatically adapting to the unknown parameters over a large collection of parameter spaces under an additional self-similarity assumption. a simulation study is carried out to illustrate the benefits of utilizing the data from the auxiliary source domains for learning in the target domain.",
"categories": "stat.ml cs.lg math.st stat.th",
"doi": "",
"created": "2022-11-22",
"updated": "2024-01-24",
"authors": [
"changxiao cai",
"t. tony cai",
"hongzhe li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.12612"
} | "2024-03-15T05:41:18.863431" | {
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},
"reason": null
}
} | {
"num_done": {
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} | [] | "algorithm" | "610bd165-ccf4-412b-99b3-38a858cb7a63" | 748 | medium |
|
\begin{algorithmic}[1]
\State Motifs = $\emptyset$
\State N = length($\textbf{T}$[0])
\Comment{Number of time series samples}
\State m = length($\textbf{T}$[0][0])
\Comment{Length of time series}
\For{$\textbf{T}_i$ $\leftarrow$ $\textbf{T}_1$ to $\textbf{T}_N$}
\State Motifs $\gets$ $\emptyset$
\For{l in [0.3m, 0.5m, 0.7m]}
\State $W_{i,l}$ $\gets$ generateCandidates($\textbf{T}_i$, l)
\For{all subsequences S in $W_{i,l}$}
\State $D_S$ $\gets$ findDistances(S, $W_{i,l}$)
\State quality $\gets$ assessCandidate(S, $D_S$)
\State Motifs.add(i,start\_idx, end\_idx, S, quality)
\Comment{The index of time series, the start idx and end idx of motifs will be stored}
\EndFor
\EndFor
\State sortByQuality(Motifs)
\EndFor
\State \Return $[[i\_0, start\_idx\_0, start\_idx\_0] , [i\_1, start\_idx\_1, start\_idx\_1]]$
\Comment{return the index information for motifs of different classes }
\end{algorithmic}
| \begin{algorithmic}
[1]
\State Motifs = $\emptyset$
\State N = length($\textbf{T}$[0])
\Comment{Number of time series samples}
\State m = length($\textbf{T}$[0][0])
\Comment{Length of time series}
\For{$\textbf{T}_i$ $\leftarrow$ $\textbf{T}_1$ to $\textbf{T}_N$}
\State Motifs $\gets$ $\emptyset$
\For{l in [0.3m, 0.5m, 0.7m]}
\State $W_{i,l}$ $\gets$ generateCandidates($\textbf{T}_i$, l)
\For{all subsequences S in $W_{i,l}$}
\State $D_S$ $\gets$ findDistances(S, $W_{i,l}$)
\State quality $\gets$ assessCandidate(S, $D_S$)
\State Motifs.add(i,start\_idx, end\_idx, S, quality)
\Comment{The index of time series, the start idx and end idx of motifs will be stored}
\EndFor
\EndFor
\State sortByQuality(Motifs)
\EndFor
\State \Return $[[i\_0, start\_idx\_0, start\_idx\_0] , [i\_1, start\_idx\_1, start\_idx\_1]]$
\Comment{return the index information for motifs of different classes }
\end{algorithmic} | "https://arxiv.org/src/2211.04411" | "2211.04411.tar.gz" | "2024-02-01" | {
"title": "motif-guided time series counterfactual explanations",
"id": "2211.04411",
"abstract": "with the rising need of interpretable machine learning methods, there is a necessity for a rise in human effort to provide diverse explanations of the influencing factors of the model decisions. to improve the trust and transparency of ai-based systems, the explainable artificial intelligence (xai) field has emerged. the xai paradigm is bifurcated into two main categories: feature attribution and counterfactual explanation methods. while feature attribution methods are based on explaining the reason behind a model decision, counterfactual explanation methods discover the smallest input changes that will result in a different decision. in this paper, we aim at building trust and transparency in time series models by using motifs to generate counterfactual explanations. we propose motif-guided counterfactual explanation (mg-cf), a novel model that generates intuitive post-hoc counterfactual explanations that make full use of important motifs to provide interpretive information in decision-making processes. to the best of our knowledge, this is the first effort that leverages motifs to guide the counterfactual explanation generation. we validated our model using five real-world time-series datasets from the ucr repository. our experimental results show the superiority of mg-cf in balancing all the desirable counterfactual explanations properties in comparison with other competing state-of-the-art baselines.",
"categories": "cs.lg",
"doi": "",
"created": "2022-11-08",
"updated": "2024-02-01",
"authors": [
"peiyu li",
"soukaina filali boubrahimi",
"shah muhammad hamdi"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.04411"
} | "2024-03-15T08:04:45.521940" | {
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} | [] | "algorithm" | "cc1709f0-b7c4-4162-a6e1-e0c3597f3e9e" | 905 | medium |
|
\begin{algorithm}[H]
\caption{Approximate Minimal Sub-Cover - 2}
\label{alg:AMSCr}
\begin{algorithmic}[1]
\State Sort the elements of $C_i$ by order of decreasing radius.
\ForAll{$(x_{i_j},r_{i_j}) \in C_i$}
\If{there does not exist $(x_{i_k}, r_{i_k}) \in C_i^*$ that covers $(x_{i_j}, r_{i_j})$}
\State Add $(x_{i_j}, r_{i_j})$ to $C_i^*$.
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{Approximate Minimal Sub-Cover - 2}
\begin{algorithmic}
[1]
\State Sort the elements of $C_i$ by order of decreasing radius.
\ForAll{$(x_{i_j},r_{i_j}) \in C_i$}
\If{there does not exist $(x_{i_k}, r_{i_k}) \in C_i^*$ that covers $(x_{i_j}, r_{i_j})$}
\State Add $(x_{i_j}, r_{i_j})$ to $C_i^*$.
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2301.09734" | "2301.09734.tar.gz" | "2024-02-08" | {
"title": "topological learning in multi-class data sets",
"id": "2301.09734",
"abstract": "we specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multi-class data set. as a by-product, a topological classifier is defined that uses an open sub-covering of the data set. this sub-covering can be used to construct a simplicial complex whose topological features (e.g., betti numbers) provide information about the classification problem. we use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (dnns). we hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. we evaluate our topological classification algorithm on multiple constructed and open source data sets. we also validate our hypothesis regarding the relationship between topological complexity and learning in dnn's on multiple data sets.",
"categories": "cs.lg physics.data-an",
"doi": "",
"created": "2023-01-23",
"updated": "2024-02-08",
"authors": [
"christopher griffin",
"trevor karn",
"benjamin apple"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2301.09734"
} | "2024-03-15T07:16:13.009881" | {
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} | [] | "algorithm" | "3ffecae1-9530-42f6-8fba-3bffa79c2654" | 374 | easy |
|
\begin{algorithm}\label{mainalgorithm} (See Algorithm 5.1 of \cite{Potra})
Given $\beta_1 < \beta_2$ with $\beta_2^2/(2(1-\beta_2)^2) \leq
\beta_1 < \beta_2 < \beta_2/(1-\beta_2) < 1$. Choose $(X_0,y_0,Y_0,
\tau_0,\kappa_0) \in \mathcal{N}(\beta_1, \mu_0)$ with $(n+1) \mu_0
= {\rm{Tr}}(X_0 Y_0) + \tau_0 \kappa_0$. For $k = 0, 1, \ldots$,
{\textcolor{black}{perform}} ($a1$) through ($a5$):
\begin{description}
\item[\hspace{5pt} ($a1$)] Set $X = X_k$, $y = y_k$, $Y = Y_k$, $\tau =
\tau_k$, $\kappa = \kappa_k$, and define
\begin{eqnarray*}
r_i & := & {\rm{Tr}}(A_i X) - b_i \tau, \quad i = 1, \ldots, m, \\
s & := & \sum_{i=1}^m y_i A_i + Y, \\
\gamma & := & \kappa - b^T y.
\end{eqnarray*}
\item[\hspace{5pt} ($a2$)] If $\max \{({\rm{Tr}}(XY) + \tau
\kappa)/\tau^2 , | r_1/\tau |, \ldots, | r_m /\tau |, \| s/\tau \| \} \leq \epsilon$, then
report $(X/\tau, y/\tau, Y/\tau)$ as an approximate solution to the LSDFP, and terminate.
If $\tau$ is sufficiently small, terminate with no optimal solutions
to the LSDFP.
\item[\hspace{5pt} ($a3$)] {\bf{[Predictor Step]}} Find the solution $(\Delta X_p,\Delta y_p, \Delta Y_p,\Delta \tau_p,
\Delta \kappa_p)$ of the linear system (\ref{sys1})-(\ref{sys5}), with
$\sigma = 0$, $\overline{r}_i = r_i, i = 1, \ldots, m$, $\overline{s} = s$ and $\overline{\gamma} = \gamma$. \newline
Define
\begin{eqnarray*}
\overline{X} = X + \overline{\alpha} \Delta X_p,\ \ \overline{y} = y + \overline{\alpha} \Delta y_p, \ \ \overline{Y} = Y +
\overline{\alpha} \Delta Y_p,\ \ \overline{\tau} = \tau +
\overline{\alpha}\Delta \tau_p,\ \ \overline{\kappa} = \kappa +
\overline{\alpha}\Delta \kappa_p,
\end{eqnarray*}
\noindent where the {\textcolor{black}{step length}} $\overline{\alpha}$ satisfies
\begin{eqnarray}\label{steplengthinequality}
\alpha_1 \leq \overline{\alpha} \leq \alpha_2.
\end{eqnarray}
Here,
\begin{eqnarray}
\alpha_1 & = & \frac{2}{\sqrt{1 + 4 \delta/(\beta_2 - \beta_1)} +1},
\label{steplengthinequality1}\\
\delta & = & \frac{1}{\mu} \left\| \left[ \begin{array}{cc}
Y & 0 \\
0 & \kappa
\end{array}\right]^{1/2}
\left[ \begin{array}{cc}
\Delta X_p & 0 \\
0 & \Delta \tau_p
\end{array} \right]
\left[ \begin{array}{cc}
\Delta Y_p & 0 \\
0 & \Delta \kappa_p
\end{array} \right]
\left[ \begin{array}{cc}
Y & 0 \\
0 & \kappa
\end{array} \right]^{-1/2} \right\|_F,
\label{steplengthinequality2}
\end{eqnarray}
where
\begin{eqnarray*}
\mu = \frac{{\rm{Tr}}(XY) + \tau \kappa}{n + 1},
\end{eqnarray*}
and
\begin{eqnarray*}
& & \alpha_2 = \max \{ \tilde{\alpha} \in [0,1] \ ; \ (X+ \alpha \Delta X_p, y + \alpha \Delta y_p, Y +
\alpha \Delta Y_p, \tau + \alpha \Delta \tau_p, \kappa + \alpha \Delta \kappa_p)
\\
& & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \in \mathcal{N}(\beta_2,(1-\alpha)\mu)\ \forall\ \alpha \in
[0,\tilde{\alpha}]\}.
\end{eqnarray*}
\item[\hspace{5pt} ($a4$)] {\bf{[Corrector Step]}} Find the solution $(\Delta X_c, \Delta y_c, \Delta Y_c, \Delta \tau_c, \Delta \kappa_c)$ of the
linear system (\ref{sys1})-(\ref{sys5}), with $\sigma = 1 -
\overline{\alpha}$, $\overline{r}_i = 0, i = 1, \ldots, m$, $\overline{s} = 0$ and $\overline{\gamma} = 0$. Set
\begin{eqnarray*}
\begin{array}{c}
X_+ = \overline{X} + \Delta X_c,\ \ y_+ = \overline{y} + \Delta y_c,\ \ Y_+ = \overline{Y} + \Delta Y_c, \ \ \tau_+ =
\overline{\tau} + \Delta \tau_c,\ \ \kappa_+ = \overline{\kappa} +
\Delta \kappa_c, \\
\mu_+ = (1 - \overline{\alpha})\mu.
\end{array}
\end{eqnarray*}
\item[\hspace{5pt} ($a5$)] Set
\begin{eqnarray*}
\begin{array}{c}
X_{k+1} = X_+,\ \ y_{k+1} = y_+, \ \ Y_{k+1} = Y_+, \ \ \tau_{k+1} = \tau_+, \ \
\kappa_{k+1} = \kappa_+,\\
\mu_{k+1} = \mu_+.
\end{array}
\end{eqnarray*}
\end{description}
\end{algorithm}
| \begin{algorithm}
(See Algorithm 5.1 of \cite{Potra})
Given $\beta_1 < \beta_2$ with $\beta_2^2/(2(1-\beta_2)^2) \leq
\beta_1 < \beta_2 < \beta_2/(1-\beta_2) < 1$. Choose $(X_0,y_0,Y_0,
\tau_0,\kappa_0) \in \mathcal{N}(\beta_1, \mu_0)$ with $(n+1) \mu_0
= {\rm{Tr}}(X_0 Y_0) + \tau_0 \kappa_0$. For $k = 0, 1, \ldots$,
{\textcolor{black}{perform}} ($a1$) through ($a5$):
\begin{description}
\item[\hspace{5pt} ($a1$)] Set $X = X_k$, $y = y_k$, $Y = Y_k$, $\tau =
\tau_k$, $\kappa = \kappa_k$, and define
\begin{eqnarray*}
r_i & := & {\rm{Tr}}(A_i X) - b_i \tau, \quad i = 1, \ldots, m, \\
s & := & \sum_{i=1}^m y_i A_i + Y, \\
\gamma & := & \kappa - b^T y.
\end{eqnarray*}
\item[\hspace{5pt} ($a2$)] If $\max \{({\rm{Tr}}(XY) + \tau
\kappa)/\tau^2 , | r_1/\tau |, \ldots, | r_m /\tau |, \| s/\tau \| \} \leq \epsilon$, then
report $(X/\tau, y/\tau, Y/\tau)$ as an approximate solution to the LSDFP, and terminate.
If $\tau$ is sufficiently small, terminate with no optimal solutions
to the LSDFP.
\item[\hspace{5pt} ($a3$)] {\bf{[Predictor Step]}} Find the solution $(\Delta X_p,\Delta y_p, \Delta Y_p,\Delta \tau_p,
\Delta \kappa_p)$ of the linear system (\ref{sys1})-(\ref{sys5}), with
$\sigma = 0$, $\overline{r}_i = r_i, i = 1, \ldots, m$, $\overline{s} = s$ and $\overline{\gamma} = \gamma$. \newline
Define
\begin{eqnarray*}
\overline{X} = X + \overline{\alpha} \Delta X_p,\ \ \overline{y} = y + \overline{\alpha} \Delta y_p, \ \ \overline{Y} = Y +
\overline{\alpha} \Delta Y_p,\ \ \overline{\tau} = \tau +
\overline{\alpha}\Delta \tau_p,\ \ \overline{\kappa} = \kappa +
\overline{\alpha}\Delta \kappa_p,
\end{eqnarray*}
\noindent where the {\textcolor{black}{step length}} $\overline{\alpha}$ satisfies
\begin{eqnarray*}
\alpha_1 \leq \overline{\alpha} \leq \alpha_2.
\end{eqnarray*}
Here,
\begin{eqnarray*}
\alpha_1 & = & \frac{2}{\sqrt{1 + 4 \delta/(\beta_2 - \beta_1)} +1},
\\
\delta & = & \frac{1}{\mu} \left\| \left[ \begin{array}
{cc}
Y & 0 \\
0 & \kappa
\end{array}\right]^{1/2}
\left[ \begin{array}
{cc}
\Delta X_p & 0 \\
0 & \Delta \tau_p
\end{array} \right]
\left[ \begin{array}
{cc}
\Delta Y_p & 0 \\
0 & \Delta \kappa_p
\end{array} \right]
\left[ \begin{array}
{cc}
Y & 0 \\
0 & \kappa
\end{array} \right]^{-1/2} \right\|_F,
\end{eqnarray*}
where
\begin{eqnarray*}
\mu = \frac{{\rm{Tr}}(XY) + \tau \kappa}{n + 1},
\end{eqnarray*}
and
\begin{eqnarray*}
& & \alpha_2 = \max \{ \tilde{\alpha} \in [0,1] \ ; \ (X+ \alpha \Delta X_p, y + \alpha \Delta y_p, Y +
\alpha \Delta Y_p, \tau + \alpha \Delta \tau_p, \kappa + \alpha \Delta \kappa_p)
\\
& & \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \in \mathcal{N}(\beta_2,(1-\alpha)\mu)\ \forall\ \alpha \in
[0,\tilde{\alpha}]\}.
\end{eqnarray*}
\item[\hspace{5pt} ($a4$)] {\bf{[Corrector Step]}} Find the solution $(\Delta X_c, \Delta y_c, \Delta Y_c, \Delta \tau_c, \Delta \kappa_c)$ of the
linear system (\ref{sys1})-(\ref{sys5}), with $\sigma = 1 -
\overline{\alpha}$, $\overline{r}_i = 0, i = 1, \ldots, m$, $\overline{s} = 0$ and $\overline{\gamma} = 0$. Set
\begin{eqnarray*}
\begin{array}
{c}
X_+ = \overline{X} + \Delta X_c,\ \ y_+ = \overline{y} + \Delta y_c,\ \ Y_+ = \overline{Y} + \Delta Y_c, \ \ \tau_+ =
\overline{\tau} + \Delta \tau_c,\ \ \kappa_+ = \overline{\kappa} +
\Delta \kappa_c, \\
\mu_+ = (1 - \overline{\alpha})\mu.
\end{array}
\end{eqnarray*}
\item[\hspace{5pt} ($a5$)] Set
\begin{eqnarray*}
\begin{array}
{c}
X_{k+1} = X_+,\ \ y_{k+1} = y_+, \ \ Y_{k+1} = Y_+, \ \ \tau_{k+1} = \tau_+, \ \
\kappa_{k+1} = \kappa_+,\\
\mu_{k+1} = \mu_+.
\end{array}
\end{eqnarray*}
\end{description}
\end{algorithm} | "https://arxiv.org/src/2211.08215" | "2211.08215.tar.gz" | "2024-01-12" | {
"title": "superlinear convergence of an interior point algorithm on linear semi-definite feasibility problems with application to linear matrix inequalities",
"id": "2211.08215",
"abstract": "in the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the hkm direction, its dual or the nt direction, to solve semi-definite programs (sdps) is shown by (i) assuming that the given sdp is nondegenerate and making modifications to these algorithms [10], or (ii) considering special classes of sdps, such as the class of linear semi-definite feasibility problems (lsdfps) and requiring the initial iterate to the algorithm to satisfy certain conditions [26, 27]. otherwise, these algorithms are not easy to implement even though they are shown to have polynomial iteration complexities and superlinear convergence [14]. the conditions in [26, 27] that the initial iterate to the algorithm is required to satisfy to have superlinear convergence when solving lsdfps however are not practical. in this paper, we propose a practical initial iterate to an implementable infeasible interior point algorithm that guarantees superlinear convergence when the algorithm is used to solve the homogeneous feasibility model of an lsdfp.",
"categories": "math.oc",
"doi": "",
"created": "2022-11-15",
"updated": "2024-01-12",
"authors": [
"chee-khian sim"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.08215"
} | "2024-03-15T06:24:29.659435" | {
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} | [] | "algorithm" | "d6e75587-aa76-4145-855f-04f2a7573dc6" | 3604 | hard |
|
\begin{algorithm}
\caption{ESTIMATE on a single interval $I_m$, i.e. time-stepping based}
\begin{algorithmic}
\Require $\hat{u}_{kh}$ on $I_{m-1}$ and $I_m$ and $\hat{z}_{kh}$ on $I_{m-1}$, $I_m$ and $I_{m+1}$
\State interpolate/reconstruct $\tilde{u}$, $u_k$, $u_{kh}$ as well as
$\tilde{z}$, $z_k$, $z_{kh}$ at quadrature points.
\State Calculate $\eta_{\star}^m$ and $\eta_\star^{m,*}$,
where $\star$ denotes $k$ or $kh$
\State Calculate $\eta_{\bullet}^{i,m}$ and $\eta_{\bullet}^{i,m,*}$ for each PU-DoF $i$ on $\mathcal{T}_h^m$,
where, again, $\bullet$ denotes $h$ or $kh$
\end{algorithmic}
\label{algo_estimate_timestep}
\end{algorithm}
| \begin{algorithm}
\caption{ESTIMATE on a single interval $I_m$, i.e. time-stepping based}
\begin{algorithmic}
\Require $\hat{u}_{kh}$ on $I_{m-1}$ and $I_m$ and $\hat{z}_{kh}$ on $I_{m-1}$, $I_m$ and $I_{m+1}$
\State interpolate/reconstruct $\tilde{u}$, $u_k$, $u_{kh}$ as well as
$\tilde{z}$, $z_k$, $z_{kh}$ at quadrature points.
\State Calculate $\eta_{\star}^m$ and $\eta_\star^{m,*}$,
where $\star$ denotes $k$ or $kh$
\State Calculate $\eta_{\bullet}^{i,m}$ and $\eta_{\bullet}^{i,m,*}$ for each PU-DoF $i$ on $\mathcal{T}_h^m$,
where, again, $\bullet$ denotes $h$ or $kh$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2207.04764" | "2207.04764.tar.gz" | "2024-02-04" | {
"title": "numerical modeling and open-source implementation of variational partition-of-unity localizations of space-time dual-weighted residual estimators for parabolic problems",
"id": "2207.04764",
"abstract": "in this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. temporal and spatial discretizations are based on galerkin finite elements of continuous and discontinuous type. the main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form employing a partition-of-unity. the resulting error indicators are used for temporal and spatial adaptivity. our developments are substantiated with several numerical examples.",
"categories": "math.na cs.na math.oc",
"doi": "",
"created": "2022-07-11",
"updated": "2024-02-04",
"authors": [
"jan philipp thiele",
"thomas wick"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2207.04764"
} | "2024-03-15T04:49:36.236742" | {
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"Intro_nonstat_PU.bib": {
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"main.out": {
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"threat_score": 0.0061296434,
"sexually_explicit_score": 0.020995872,
"flirtation_score": 0.40309274
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},
"reason": null
}
} | {
"num_done": {
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"algorithm": 3
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} | [] | "algorithm" | "2db594cd-07bf-4cb3-9bdb-45c1106c895a" | 612 | easy |
|
\begin{algorithm}
\caption{Bernoulli factory for continuous $f : [0, 1] \mapsto [0, 1]$ satisfying \eqref{polynomially_bounded}.}
\label{alg_1}
\begin{algorithmic}[1]
\Require Sequences $\{ f_k \}_{k \geq 1}$, $\{ \eta( f, k ) \}_{k \geq 1}$.
\State Sample $L \sim \operatorname{Geo}(1 / 4)$.
\State Sample $X_{\eta( f, L ) }( p ) \sim \operatorname{Bin}( \eta( f, L ), p )$.
\If{$f_L( X_{\eta( f, L ) } ( p ) / L ) \geq 1/2$}
\State Return 1.
\Else
\State Return 0.
\EndIf
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Bernoulli factory for continuous $f : [0, 1] \mapsto [0, 1]$ satisfying \eqref{polynomially_bounded}.}
\begin{algorithmic}
[1]
\Require Sequences $\{ f_k \}_{k \geq 1}$, $\{ \eta( f, k ) \}_{k \geq 1}$.
\State Sample $L \sim \operatorname{Geo}(1 / 4)$.
\State Sample $X_{\eta( f, L ) }( p ) \sim \operatorname{Bin}( \eta( f, L ), p )$.
\If{$f_L( X_{\eta( f, L ) } ( p ) / L ) \geq 1/2$}
\State Return 1.
\Else
\State Return 0.
\EndIf
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2306.03539" | "2306.03539.tar.gz" | "2024-02-01" | {
"title": "bernoulli factories and duality in wright-fisher and allen-cahn models of population genetics",
"id": "2306.03539",
"abstract": "mathematical models of genetic evolution often come in pairs, connected by a so-called duality relation. the most seminal example are the wright-fisher diffusion and the kingman coalescent, where the former describes the stochastic evolution of neutral allele frequencies in a large population forwards in time, and the latter describes the genetic ancestry of randomly sampled individuals from the population backwards in time. as well as providing a richer description than either model in isolation, duality often yields equations satisfied by quantities of interest. we employ the so-called bernoulli factory - a celebrated tool in simulation-based computing - to derive duality relations for broad classes of genetics models. as concrete examples, we present wright-fisher diffusions with general drift functions, and allen-cahn equations with general, nonlinear forcing terms. the drift and forcing functions can be interpreted as the action of frequency-dependent selection. to our knowledge, this work is the first time a connection has been drawn between bernoulli factories and duality in models of population genetics.",
"categories": "math.pr q-bio.pe",
"doi": "",
"created": "2023-06-06",
"updated": "2024-02-01",
"authors": [
"jere koskela",
"krzysztof \u0142atuszy\u0144ski",
"dario span\u00f2"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2306.03539"
} | "2024-03-15T05:56:16.398949" | {
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} | [] | "algorithm" | "e3e1d65e-83c7-4b98-ade5-fcdf139940ad" | 494 | easy |
|
\begin{algorithmic}
\State $e_1$ = Minimized energy wrt vertex positions
\State Swap cells i and j
\State $e_2$ = Minimized energy wrt vertex positions
\If{$e_2 < e_1$}
\State Accept this swap move
\Else
\State Reject this swap move
\EndIf
\end{algorithmic}
| \begin{algorithmic}
\State $e_1$ = Minimized energy wrt vertex positions
\State Swap cells i and j
\State $e_2$ = Minimized energy wrt vertex positions
\If{$e_2 < e_1$}
\State Accept this swap move
\Else
\State Reject this swap move
\EndIf
\end{algorithmic} | "https://arxiv.org/src/2312.11683" | "2312.11683.tar.gz" | "2024-01-07" | {
"title": "tuning for fluidity using fluctuations in biological tissue models",
"id": "2312.11683",
"abstract": "how do biological systems tune emergent properties at the scale of tissues? one class of such emergent behaviors, important to biological functions such as body-axis elongation, involves rigidity transitions, in which a tissue changes from a fluid-like state to a solid-like state or vice versa. here, we explore the idea that tissues might tune ``learning degrees of freedom\" to affect this emergent behavior. we study tissue fluidity in the 2d vertex model, using the vertex model energy as a learning cost function and the cell stiffnesses, target shapes, and target areas as sets of learning degrees of freedom that can be varied to minimize the energy. we show that the rigidity transition is unaffected when cell stiffnesses are treated as learning degrees of freedom. when preferred perimeters or areas are treated as learning degrees of freedom, however, energy minimization introduces spatial correlations in target cell shapes or areas that shift the rigidity transition. there is an optimal heterogeneity of target cell shapes or areas to enable learning. these observations suggest that biological tissues can learn tissue-scale behaviors by tuning their individual cell properties.",
"categories": "cond-mat.soft physics.bio-ph q-bio.to",
"doi": "",
"created": "2023-12-18",
"updated": "2024-01-07",
"authors": [
"sadjad arzash",
"indrajit tah",
"andrea j. liu",
"m. lisa manning"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.11683"
} | "2024-03-15T07:49:18.144761" | {
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}
} | {
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} | [] | "algorithm" | "5a73de89-9917-4d1c-8f2b-836f173ac6c8" | 257 | easy |
|
\label{alg:UCB-TL} \begin{algorithmic}[1]
\State{\textbf{Input:} arm set $\mathcal{I}$, horizon length
$n_{Q}$, smoothness parameters $\beta, C_{\beta}$, transfer parameters $\gamma$, exploration coefficient $\kappa$, $P$-data $\mathcal{D}^{P}$.}
\State{Initialize $\mathcal{L}_{1}\gets\{\mathcal{X}\}$, $\mathcal{I}(\mathcal{X})\gets\mathcal{I}$.}
\Comment{initialize partition and arm set}
\State{Initialize the policy $\widetilde{\pi}(\mathcal{X})$ by Procedure~\ref{alg:EA-TL}$\big(\mathcal{X},\mathcal{I}(\mathcal{X}),U,\mathcal{D}^{P} \big)$.}
\State{Initialize $N(\mathcal{X})\gets0$.}
\Comment{initialize time for policy $\widetilde{\pi}(\mathcal{X})$}
\State{Initialize $\tau_{k}(\mathcal{X}) \gets 0$, and $\tau_{k}^{\star}(\mathcal{X};\mathcal{D}^{P}) $ as in \eqref{eq:tau-star}, $\forall k\in \mathcal{I}(\mathcal{X})$.}
\Comment{initialize rounds and set round upper bounds}
\For{$t=1,\dots,n_{Q}$}
\State{Draw a sample $X_{t}^{Q} \sim Q_{X}$.}
\State{Find the bin $B\in\mathcal{L}_{t}$ such that $X_{t}^{Q}\in B$.}
\While{$|\mathcal{I}(B)|>1$
and $\tau_{k}(B)\geq\tau_{k}^{\star}(B;\mathcal{D}^{P}), \forall k\in\mathcal{I}(B)$}
\Comment{keep partitioning $B$ until reaching suitable scale}
\If{$\tau_{k}^{\star}(B;\mathcal{D}^{P}) = 0, \forall k\in\mathcal{I}(B)$}
\Comment{no exploration needed in $B$: discard suboptimal arms}
\State{Set $\underline{Y}^{\star}(B;\mathcal{D}^{P})\gets\max\limits_{k\in\mathcal{I}(B)}\big\{\overline{Y}_{k}^P(B;\mathcal{D}^{P})- U_{k}(0,B;\mathcal{D}^{P}) \big\}$.}
\Comment{set largest reward lower bound}
\State{Set $\mathcal{I}(B) \gets \big\{ k \in \mathcal{I}(B) : \overline{Y}_k^P(B;\mathcal{D}^{P})+U_{k}(0,B;\mathcal{D}^{P}) \geq \underline{Y}^{\star}(B;\mathcal{D}^{P}) \big\}$.}
\Comment{update arm set}
\EndIf
\For{$B'\in\mathsf{child}(B)$}
\State{Set $\mathcal{I}(B')\gets\mathcal{I}(B)$.}
\Comment{assign remaining arms in $B$ as initial arms in its children}
\State{Initialize the policy $\widetilde{\pi}(B')$ by Procedure~\ref{alg:EA-TL} $ \big(B',\mathcal{I}(B'),U,\mathcal{D}^{P} \big)$.}
\State{Set $N(B')\gets0$.}
\Comment{initialize time for policy $\widetilde{\pi}(B')$}
\State{Set $\tau_{k}(B')\gets0$ and $\tau_{k}^{\star}(B';\mathcal{D}^{P})$ as in \eqref{eq:tau-star}, $\forall k\in\mathcal{I}(B')$.}
\Comment{initialize rounds and set round upper bounds}
\EndFor
\State{Set $\mathcal{L}_{t}\gets (\mathcal{L}_{t}\setminus B)\cup\mathsf{child}(B)$.}
\Comment{replace $B$ with its children in partition}
\State{Find the bin $B\in\mathcal{L}_{t}$ such that $ X_{t}^{Q}\in B$.}
\EndWhile
\State{Set $N(B)\gets N(B)+1$.}
\Comment{update times $X_{t}^{Q} \in B$}
\State{Set $\pi_{t}\gets\widetilde{\pi}_{N(B)}(B)$.}
\Comment{choose arm by policy $\widetilde{\pi}(B)$}
\State{Set $\mathcal{I}(B)\gets\widetilde{\mathcal{I}}_{N(B)} (B)$.}
\Comment{update arm set by policy $\widetilde{\pi}(B)$}
\State{Set $\tau_{k}(B) \gets \widetilde{\tau}_{N(B),k}(B), \forall k\in\mathcal{I}(B)$.}
\Comment{update numbers of rounds by policy $\widetilde{\pi}(B)$}
\EndFor
\State{\textbf{Output:} policy $\{\pi_{t}\}_{t\geq1}$.}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State{\textbf{Input:} arm set $\mathcal{I}$, horizon length
$n_{Q}$, smoothness parameters $\beta, C_{\beta}$, transfer parameters $\gamma$, exploration coefficient $\kappa$, $P$-data $\mathcal{D}^{P}$.}
\State{Initialize $\mathcal{L}_{1}\gets\{\mathcal{X}\}$, $\mathcal{I}(\mathcal{X})\gets\mathcal{I}$.}
\Comment{initialize partition and arm set}
\State{Initialize the policy $\widetilde{\pi}(\mathcal{X})$ by Procedure~\ref{alg:EA-TL}$\big(\mathcal{X},\mathcal{I}(\mathcal{X}),U,\mathcal{D}^{P} \big)$.}
\State{Initialize $N(\mathcal{X})\gets0$.}
\Comment{initialize time for policy $\widetilde{\pi}(\mathcal{X})$}
\State{Initialize $\tau_{k}(\mathcal{X}) \gets 0$, and $\tau_{k}^{\star}(\mathcal{X};\mathcal{D}^{P}) $ as in \eqref{eq:tau-star}, $\forall k\in \mathcal{I}(\mathcal{X})$.}
\Comment{initialize rounds and set round upper bounds}
\For{$t=1,\dots,n_{Q}$}
\State{Draw a sample $X_{t}^{Q} \sim Q_{X}$.}
\State{Find the bin $B\in\mathcal{L}_{t}$ such that $X_{t}^{Q}\in B$.}
\While{$|\mathcal{I}(B)|>1$
and $\tau_{k}(B)\geq\tau_{k}^{\star}(B;\mathcal{D}^{P}), \forall k\in\mathcal{I}(B)$}
\Comment{keep partitioning $B$ until reaching suitable scale}
\If{$\tau_{k}^{\star}(B;\mathcal{D}^{P}) = 0, \forall k\in\mathcal{I}(B)$}
\Comment{no exploration needed in $B$: discard suboptimal arms}
\State{Set $\underline{Y}^{\star}(B;\mathcal{D}^{P})\gets\max\limits_{k\in\mathcal{I}(B)}\big\{\overline{Y}_{k}^P(B;\mathcal{D}^{P})- U_{k}(0,B;\mathcal{D}^{P}) \big\}$.}
\Comment{set largest reward lower bound}
\State{Set $\mathcal{I}(B) \gets \big\{ k \in \mathcal{I}(B) : \overline{Y}_k^P(B;\mathcal{D}^{P})+U_{k}(0,B;\mathcal{D}^{P}) \geq \underline{Y}^{\star}(B;\mathcal{D}^{P}) \big\}$.}
\Comment{update arm set}
\EndIf
\For{$B'\in\mathsf{child}(B)$}
\State{Set $\mathcal{I}(B')\gets\mathcal{I}(B)$.}
\Comment{assign remaining arms in $B$ as initial arms in its children}
\State{Initialize the policy $\widetilde{\pi}(B')$ by Procedure~\ref{alg:EA-TL} $ \big(B',\mathcal{I}(B'),U,\mathcal{D}^{P} \big)$.}
\State{Set $N(B')\gets0$.}
\Comment{initialize time for policy $\widetilde{\pi}(B')$}
\State{Set $\tau_{k}(B')\gets0$ and $\tau_{k}^{\star}(B';\mathcal{D}^{P})$ as in \eqref{eq:tau-star}, $\forall k\in\mathcal{I}(B')$.}
\Comment{initialize rounds and set round upper bounds}
\EndFor
\State{Set $\mathcal{L}_{t}\gets (\mathcal{L}_{t}\setminus B)\cup\mathsf{child}(B)$.}
\Comment{replace $B$ with its children in partition}
\State{Find the bin $B\in\mathcal{L}_{t}$ such that $ X_{t}^{Q}\in B$.}
\EndWhile
\State{Set $N(B)\gets N(B)+1$.}
\Comment{update times $X_{t}^{Q} \in B$}
\State{Set $\pi_{t}\gets\widetilde{\pi}_{N(B)}(B)$.}
\Comment{choose arm by policy $\widetilde{\pi}(B)$}
\State{Set $\mathcal{I}(B)\gets\widetilde{\mathcal{I}}_{N(B)} (B)$.}
\Comment{update arm set by policy $\widetilde{\pi}(B)$}
\State{Set $\tau_{k}(B) \gets \widetilde{\tau}_{N(B),k}(B), \forall k\in\mathcal{I}(B)$.}
\Comment{update numbers of rounds by policy $\widetilde{\pi}(B)$}
\EndFor
\State{\textbf{Output:} policy $\{\pi_{t}\}_{t\geq1}$.}
\end{algorithmic} | "https://arxiv.org/src/2211.12612" | "2211.12612.tar.gz" | "2024-01-24" | {
"title": "transfer learning for contextual multi-armed bandits",
"id": "2211.12612",
"abstract": "motivated by a range of applications, we study in this paper the problem of transfer learning for nonparametric contextual multi-armed bandits under the covariate shift model, where we have data collected on source bandits before the start of the target bandit learning. the minimax rate of convergence for the cumulative regret is established and a novel transfer learning algorithm that attains the minimax regret is proposed. the results quantify the contribution of the data from the source domains for learning in the target domain in the context of nonparametric contextual multi-armed bandits. in view of the general impossibility of adaptation to unknown smoothness, we develop a data-driven algorithm that achieves near-optimal statistical guarantees (up to a logarithmic factor) while automatically adapting to the unknown parameters over a large collection of parameter spaces under an additional self-similarity assumption. a simulation study is carried out to illustrate the benefits of utilizing the data from the auxiliary source domains for learning in the target domain.",
"categories": "stat.ml cs.lg math.st stat.th",
"doi": "",
"created": "2022-11-22",
"updated": "2024-01-24",
"authors": [
"changxiao cai",
"t. tony cai",
"hongzhe li"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2211.12612"
} | "2024-03-15T05:41:18.863431" | {
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} | [] | "algorithm" | "30c4349b-761b-4614-b9c0-1247edaaaf90" | 3082 | hard |
|
\begin{algorithmic}[1]
\State {\bfseries } Learned topics $T$ as references
\State {\bfseries }\textbf{for} i = 1,2,$\cdots$, N \textbf{do}
\State {\bfseries } \quad Automatically transcribe dialogue turn pairs $(S^p_i,S^t_i)$
\State {\bfseries }\quad \textbf{for} $T_j \in$ topics $T$ \textbf{do}
\State {\bfseries }\quad \quad Topic score $W^{p_i}_{j}$ = similarity($Emb({T_j}), Emb(S^p_i)$)
\State {\bfseries }\quad \quad Topic score $W^{t_i}_{j}$ = similarity($Emb({T_j}), Emb(S^t_i)$)
\State {\bfseries } \quad \textbf{end for}
\State {\bfseries } \textbf{end for}
\end{algorithmic}
| \begin{algorithmic}
[1]
\State {\bfseries } Learned topics $T$ as references
\State {\bfseries }\textbf{for} i = 1,2,$\cdots$, N \textbf{do}
\State {\bfseries } \quad Automatically transcribe dialogue turn pairs $(S^p_i,S^t_i)$
\State {\bfseries }\quad \textbf{for} $T_j \in$ topics $T$ \textbf{do}
\State {\bfseries }\quad \quad Topic score $W^{p_i}_{j}$ = similarity($Emb({T_j}), Emb(S^p_i)$)
\State {\bfseries }\quad \quad Topic score $W^{t_i}_{j}$ = similarity($Emb({T_j}), Emb(S^t_i)$)
\State {\bfseries } \quad \textbf{end for}
\State {\bfseries } \textbf{end for}
\end{algorithmic} | "https://arxiv.org/src/2402.14701" | "2402.14701.tar.gz" | "2024-02-22" | {
"title": "compass: computational mapping of patient-therapist alliance strategies with language modeling",
"id": "2402.14701",
"abstract": "the therapeutic working alliance is a critical factor in predicting the success of psychotherapy treatment. traditionally, working alliance assessment relies on questionnaires completed by both therapists and patients. in this paper, we present compass, a novel framework to directly infer the therapeutic working alliance from the natural language used in psychotherapy sessions. our approach utilizes advanced large language models to analyze transcripts of psychotherapy sessions and compare them with distributed representations of statements in the working alliance inventory. analyzing a dataset of over 950 sessions covering diverse psychiatric conditions, we demonstrate the effectiveness of our method in microscopically mapping patient-therapist alignment trajectories and providing interpretability for clinical psychiatry and in identifying emerging patterns related to the condition being treated. by employing various neural topic modeling techniques in combination with generative language prompting, we analyze the topical characteristics of different psychiatric conditions and incorporate temporal modeling to capture the evolution of topics at a turn-level resolution. this combined framework enhances the understanding of therapeutic interactions, enabling timely feedback for therapists regarding conversation quality and providing interpretable insights to improve the effectiveness of psychotherapy.",
"categories": "cs.cl cs.ai cs.hc cs.lg q-bio.nc",
"doi": "",
"created": "2024-02-22",
"updated": "",
"authors": [
"baihan lin",
"djallel bouneffouf",
"yulia landa",
"rachel jespersen",
"cheryl corcoran",
"guillermo cecchi"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.14701"
} | "2024-03-15T03:37:09.328472" | {
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} | [] | "algorithm" | "53dbce17-15be-4982-b262-83e99c02bec4" | 588 | easy |
|
\begin{algorithmic}[1]
\Require
\Statex$\tau$: Scale of coordinate noise
\Statex$GNN_{\theta}$: Graph Neural Network with parameter $\theta$
\Statex ${\rm NoiseHead}_{\theta_{n}}$: Network module with parameter $\theta_{n}$ for prediction of node-level noise of each atom
\Statex ${\rm LabelHead}_{\theta_{l}}$: Network module with parameter $\theta_{l}$ for prediction of graph-level label of $x_{i}$
\Statex$X$: Training dataset
\Statex$x_i$: Input conformation
\Statex$y_i$: Label of $x_i$
\Statex$T$: Training steps
\Statex$\mathcal N$: Gaussian distribution
\Statex$\lambda_{p}$: Loss weight of property prediction loss
\Statex$\lambda_{n}$: Loss weight of Noisy Nodes loss
\While{$T \neq 0$}
\State $x_i, y_i$ = dataloader($X$) \Comment{random sample $x_i$ and corresponding label $y_i$ from $X$}
\State $\tilde{x} = x_{i} + \Delta{x_i}$ , where $\Delta{x_i} \sim \mathcal{N}(0, {\tau}^2I_{3N})$, $N$ is atom number of $x_i$
\State $y_{i}^{pred}={\rm LabelHead}_{\theta_{l}}(GNN_{\theta}(\tilde{x}))$
\State $\Delta{x_i}^{pred}={\rm NoiseHead}_{\theta_{n}}(GNN_{\theta}(\tilde{x}))$
\State Loss = $\lambda_{p}$PropertyPredictionLoss$(y_{i}^{pred}, y_i)$+$\lambda_{n}||\Delta{x_i}^{pred} - \Delta{x_i}||_{2}^{2}$
\State Optimise(Loss)
\State $T = T - 1$
\EndWhile
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require
\Statex$\tau$: Scale of coordinate noise
\Statex$GNN_{\theta}$: Graph Neural Network with parameter $\theta$
\Statex ${\rm NoiseHead}_{\theta_{n}}$: Network module with parameter $\theta_{n}$ for prediction of node-level noise of each atom
\Statex ${\rm LabelHead}_{\theta_{l}}$: Network module with parameter $\theta_{l}$ for prediction of graph-level label of $x_{i}$
\Statex$X$: Training dataset
\Statex$x_i$: Input conformation
\Statex$y_i$: Label of $x_i$
\Statex$T$: Training steps
\Statex$\mathcal N$: Gaussian distribution
\Statex$\lambda_{p}$: Loss weight of property prediction loss
\Statex$\lambda_{n}$: Loss weight of Noisy Nodes loss
\While{$T \neq 0$}
\State $x_i, y_i$ = dataloader($X$) \Comment{random sample $x_i$ and corresponding label $y_i$ from $X$}
\State $\tilde{x} = x_{i} + \Delta{x_i}$ , where $\Delta{x_i} \sim \mathcal{N}(0, {\tau}^2I_{3N})$, $N$ is atom number of $x_i$
\State $y_{i}^{pred}={\rm LabelHead}_{\theta_{l}}(GNN_{\theta}(\tilde{x}))$
\State $\Delta{x_i}^{pred}={\rm NoiseHead}_{\theta_{n}}(GNN_{\theta}(\tilde{x}))$
\State Loss = $\lambda_{p}$PropertyPredictionLoss$(y_{i}^{pred}, y_i)$+$\lambda_{n}||\Delta{x_i}^{pred} - \Delta{x_i}||_{2}^{2}$
\State Optimise(Loss)
\State $T = T - 1$
\EndWhile
\end{algorithmic} | "https://arxiv.org/src/2307.10683" | "2307.10683.tar.gz" | "2024-02-26" | {
"title": "fractional denoising for 3d molecular pre-training",
"id": "2307.10683",
"abstract": "coordinate denoising is a promising 3d molecular pre-training method, which has achieved remarkable performance in various downstream drug discovery tasks. theoretically, the objective is equivalent to learning the force field, which is revealed helpful for downstream tasks. nevertheless, there are two challenges for coordinate denoising to learn an effective force field, i.e. low coverage samples and isotropic force field. the underlying reason is that molecular distributions assumed by existing denoising methods fail to capture the anisotropic characteristic of molecules. to tackle these challenges, we propose a novel hybrid noise strategy, including noises on both dihedral angel and coordinate. however, denoising such hybrid noise in a traditional way is no more equivalent to learning the force field. through theoretical deductions, we find that the problem is caused by the dependency of the input conformation for covariance. to this end, we propose to decouple the two types of noise and design a novel fractional denoising method (frad), which only denoises the latter coordinate part. in this way, frad enjoys both the merits of sampling more low-energy structures and the force field equivalence. extensive experiments show the effectiveness of frad in molecular representation, with a new state-of-the-art on 9 out of 12 tasks of qm9 and on 7 out of 8 targets of md17.",
"categories": "q-bio.qm cs.lg physics.chem-ph",
"doi": "",
"created": "2023-07-20",
"updated": "2024-02-26",
"authors": [
"shikun feng",
"yuyan ni",
"yanyan lan",
"zhi-ming ma",
"wei-ying ma"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2307.10683"
} | "2024-03-15T02:31:31.211598" | {
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} | [] | "algorithm" | "7e1c230e-b2f9-46cb-9d37-e0e427b71cca" | 1287 | hard |
|
\begin{algorithmic}[1]
\Statex Input: The underlying linear dynamical systems matrices $\tilde{B}$ and $\tilde{B'}$ and the correlations between each of the coordinates (corresponding to genes) and the two phenotypes of interest.
\Statex Output: A set of pathways of a given length $L$ that are prominently different between the two phenotypes.
\Statex $\triangleright$ Algorithm starts:
\State Compute and sort the list of genes in descending order in terms of the absolute value of their correlation coefficient with the pathological phenotype, denote this list as $\vec{g}$
\State Compute $C:= \mathrm{Diag}(\vec{g})(\tilde{B'}-\tilde{B})$
\State Fix a positive threshold $\theta$ and set $C_{ij}=0$ if $C_{ij}<\theta$, denote the resulting matrix as $\Pi_\theta$
\State Compute the set of paths of length $L$ in the graph with adjacency matrix $\Pi_\theta$ and return them.
\end{algorithmic}
| \begin{algorithmic}
[1]
\Statex Input: The underlying linear dynamical systems matrices $\tilde{B}$ and $\tilde{B'}$ and the correlations between each of the coordinates (corresponding to genes) and the two phenotypes of interest.
\Statex Output: A set of pathways of a given length $L$ that are prominently different between the two phenotypes.
\Statex $\triangleright$ Algorithm starts:
\State Compute and sort the list of genes in descending order in terms of the absolute value of their correlation coefficient with the pathological phenotype, denote this list as $\vec{g}$
\State Compute $C:= \mathrm{Diag}(\vec{g})(\tilde{B'}-\tilde{B})$
\State Fix a positive threshold $\theta$ and set $C_{ij}=0$ if $C_{ij}<\theta$, denote the resulting matrix as $\Pi_\theta$
\State Compute the set of paths of length $L$ in the graph with adjacency matrix $\Pi_\theta$ and return them.
\end{algorithmic} | "https://arxiv.org/src/2401.11858" | "2401.11858.tar.gz" | "2024-01-22" | {
"title": "approximating a linear dynamical system from non-sequential data",
"id": "2401.11858",
"abstract": "given non-sequential snapshots from instances of a dynamical system, we design a compressed sensing based algorithm that reconstructs the dynamical system. we formally prove that successful reconstruction is possible under the assumption that we can construct an approximate clock from a subset of the coordinates of the underlying system. as an application, we argue that our assumption is likely true for genomic datasets, and we recover the underlying nuclear receptor networks and predict pathways, as opposed to genes, that may differentiate phenotypes in some publicly available datasets.",
"categories": "q-bio.gn",
"doi": "",
"created": "2024-01-22",
"updated": "",
"authors": [
"cliff stein",
"pratik worah"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.11858"
} | "2024-03-15T07:04:04.342410" | {
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} | [] | "algorithm" | "6712150d-8079-4798-b74b-d08a5d1ff345" | 896 | medium |
|
\begin{algorithm}
\caption{Anchored MFL-DA}\label{alg:cap}
\begin{algorithmic}
\For{$\ell =0,\cdots,T_\text{out}-1$}
\For{$k=0,\cdots,T_\text{in}-1$} (concurrently for all $s\in\mathcal{S}$)
\State $\theta_{k+1}^{(i)} \gets (1-\eta\lambda)\theta_k^{(i)}-2\eta \nabla_{\theta,k}^{(i)}+\eta\widetilde{\nabla}_\theta^{(i)} +\sqrt{2\lambda\eta} \cdot\omega_k^{(i)}$, $\omega_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
\State $\phi_{k+1}^{(i)} \gets (1-\eta\lambda)\phi_k^{(i)}+2\eta \nabla_{\phi,k}^{(i)}-\eta\widetilde{\nabla}_\phi^{(i)} +\sqrt{2\lambda\eta} \cdot\beta_k^{(i)}$, $\beta_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
\State (computed with respect to the current action-value network $Q_\ell$)
\If{$k$ mod $K \equiv 0$}
\State $\widetilde{\nabla}_\theta^{(i)}, \widetilde{\nabla}_\phi^{(i)} \gets \nabla_{\theta,k}^{(i)}, \nabla_{\phi,k}^{(i)}$
\EndIf
\EndFor
\State perform some TD learning update $(Q_{\ell+1}(x,y|s))_{s\in\mathcal{S}}\gets (Q_\ell(x,y|s))_{s\in\mathcal{S}}$ using $\theta_{T_\text{in}}, \phi_{T_\text{in}}$
\EndFor
\Return $Q_{T_\text{out}}, \theta_{T_\text{in}}, \phi_{T_\text{in}}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Anchored MFL-DA}\begin{algorithmic}
\For{$\ell =0,\cdots,T_\text{out}-1$}
\For{$k=0,\cdots,T_\text{in}-1$} (concurrently for all $s\in\mathcal{S}$)
\State $\theta_{k+1}^{(i)} \gets (1-\eta\lambda)\theta_k^{(i)}-2\eta \nabla_{\theta,k}^{(i)}+\eta\widetilde{\nabla}_\theta^{(i)} +\sqrt{2\lambda\eta} \cdot\omega_k^{(i)}$, $\omega_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
\State $\phi_{k+1}^{(i)} \gets (1-\eta\lambda)\phi_k^{(i)}+2\eta \nabla_{\phi,k}^{(i)}-\eta\widetilde{\nabla}_\phi^{(i)} +\sqrt{2\lambda\eta} \cdot\beta_k^{(i)}$, $\beta_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
\State (computed with respect to the current action-value network $Q_\ell$)
\If{$k$ mod $K \equiv 0$}
\State $\widetilde{\nabla}_\theta^{(i)}, \widetilde{\nabla}_\phi^{(i)} \gets \nabla_{\theta,k}^{(i)}, \nabla_{\phi,k}^{(i)}$
\EndIf
\EndFor
\State perform some TD learning update $(Q_{\ell+1}(x,y|s))_{s\in\mathcal{S}}\gets (Q_\ell(x,y|s))_{s\in\mathcal{S}}$ using $\theta_{T_\text{in}}, \phi_{T_\text{in}}$
\EndFor
\Return $Q_{T_\text{out}}, \theta_{T_\text{in}}, \phi_{T_\text{in}}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2312.01127" | "2312.01127.tar.gz" | "2024-02-16" | {
"title": "symmetric mean-field langevin dynamics for distributional minimax problems",
"id": "2312.01127",
"abstract": "in this paper, we extend mean-field langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. we propose mean-field langevin averaged gradient (mfl-ag), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed nash equilibrium. we also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. furthermore, we propose mean-field langevin anchored best response (mfl-abr), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. finally, we study applications to zero-sum markov games and conduct simulations demonstrating long-term optimality.",
"categories": "math.oc stat.ml",
"doi": "",
"created": "2023-12-02",
"updated": "2024-02-16",
"authors": [
"juno kim",
"kakei yamamoto",
"kazusato oko",
"zhuoran yang",
"taiji suzuki"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.01127"
} | "2024-03-15T05:16:00.811582" | {
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} | [] | "algorithm" | "8cf050b7-602d-453a-9cf8-4c7c2439fd12" | 1120 | medium |
|
\begin{algorithm}[htb]
\caption{Forward propagation for each convolutional 3D layer. $M_w$, $\Sigma_w$ are the means and variances of each layer, $H$ is the input layer, and NF(·) is the masked
RealNVP normalising flow applied over samples initially drawn from a Gaussian distribution $q$. $D_f$ is the number of filters for each kernel. $\odot$ corresponds to element-wise multiplication.}
\label{alg:conv_bnn3d}
\begin{algorithmic}
\State $\text{Input: feature vector of the previous layer (minibatch)}$
\State $H \gets \text{Input conv3D-layer (minibatch)}$
\State $\*z_0 \sim q(\*z_0)$
\State $\*z_{T_f} = \text{NF}(\*z_0)$
\State $\*M_h = \*H * (\*M_w \odot \text{reshape}(\*z_{T_f}, [1,1, 1, D_f]))$
\State $\*V_h = \*H^2 * \!\Sigma_w$
\State $\*E \sim \mathcal{N}(0, 1)$
\State return $\*M_h + \sqrt{\*V_h} \odot \*E$
\State$\text{Output: sample of feature vector according to Eq.~\ref{mnfpos3d}}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[htb]
\caption{Forward propagation for each convolutional 3D layer. $M_w$, $\Sigma_w$ are the means and variances of each layer, $H$ is the input layer, and NF(·) is the masked
RealNVP normalising flow applied over samples initially drawn from a Gaussian distribution $q$. $D_f$ is the number of filters for each kernel. $\odot$ corresponds to element-wise multiplication.}
\begin{algorithmic}
\State $\text{Input: feature vector of the previous layer (minibatch)}$
\State $H \gets \text{Input conv3D-layer (minibatch)}$
\State $\*z_0 \sim q(\*z_0)$
\State $\*z_{T_f} = \text{NF}(\*z_0)$
\State $\*M_h = \*H * (\*M_w \odot \text{reshape}(\*z_{T_f}, [1,1, 1, D_f]))$
\State $\*V_h = \*H^2 * \!\Sigma_w$
\State $\*E \sim \mathcal{N}(0, 1)$
\State return $\*M_h + \sqrt{\*V_h} \odot \*E$
\State$\text{Output: sample of feature vector according to Eq.~\ref{mnfpos3d}}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2309.00612" | "2309.00612.tar.gz" | "2024-02-12" | {
"title": "bayesian deep learning for cosmic volumes with modified gravity",
"id": "2309.00612",
"abstract": "the new generation of galaxy surveys will provide unprecedented data allowing us to test gravity at cosmological scales. a robust cosmological analysis of the large-scale structure demands exploiting the nonlinear information encoded in the cosmic web. machine learning techniques provide such tools, however, do not provide a priori assessment of uncertainties. this study aims at extracting cosmological parameters from modified gravity (mg) simulations through deep neural networks endowed with uncertainty estimations. we implement bayesian neural networks (bnns) with an enriched approximate posterior distribution considering two cases: one with a single bayesian last layer (bll), and another one with bayesian layers at all levels (fullb). we train both bnns with real-space density fields and power-spectra from a suite of 2000 dark matter only particle mesh $n$-body simulations including modified gravity models relying on mg-picola covering 256 $h^{-1}$ mpc side cubical volumes with 128$^3$ particles. bnns excel in accurately predicting parameters for $\\omega_m$ and $\\sigma_8$ and their respective correlation with the mg parameter. we find out that bnns yield well-calibrated uncertainty estimates overcoming the over- and under-estimation issues in traditional neural networks. we observe that the presence of mg parameter leads to a significant degeneracy with $\\sigma_8$ being one of the possible explanations of the poor mg predictions. ignoring mg, we obtain a deviation of the relative errors in $\\omega_m$ and $\\sigma_8$ by at least $30\\%$. moreover, we report consistent results from the density field and power spectra analysis, and comparable results between bll and fullb experiments which permits us to save computing time by a factor of two. this work contributes in setting the path to extract cosmological parameters from complete small cosmic volumes towards the highly nonlinear regime.",
"categories": "astro-ph.co astro-ph.im cs.lg stat.ml",
"doi": "10.1051/0004-6361/202347929",
"created": "2023-09-01",
"updated": "2024-02-12",
"authors": [
"jorge enrique garc\u00eda-farieta",
"h\u00e9ctor j hort\u00faa",
"francisco-shu kitaura"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2309.00612"
} | "2024-03-15T06:33:59.935340" | {
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} | [] | "algorithm" | "cfe5e46c-8548-48bf-a2f1-e941bdbb3275" | 916 | medium |
|
\begin{algorithmic}
\For{$\ell =0,\cdots,T_\text{out}-1$}
\For{$k=0,\cdots,T_\text{in}-1$} (concurrently for all $s\in\mathcal{S}$)
\State $\theta_{k+1}^{(i)} \gets (1-\eta\lambda)\theta_k^{(i)}-2\eta \nabla_{\theta,k}^{(i)}+\eta\widetilde{\nabla}_\theta^{(i)} +\sqrt{2\lambda\eta} \cdot\omega_k^{(i)}$, $\omega_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
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\State (computed with respect to the current action-value network $Q_\ell$)
\If{$k$ mod $K \equiv 0$}
\State $\widetilde{\nabla}_\theta^{(i)}, \widetilde{\nabla}_\phi^{(i)} \gets \nabla_{\theta,k}^{(i)}, \nabla_{\phi,k}^{(i)}$
\EndIf
\EndFor
\State perform some TD learning update $(Q_{\ell+1}(x,y|s))_{s\in\mathcal{S}}\gets (Q_\ell(x,y|s))_{s\in\mathcal{S}}$ using $\theta_{T_\text{in}}, \phi_{T_\text{in}}$
\EndFor
\Return $Q_{T_\text{out}}, \theta_{T_\text{in}}, \phi_{T_\text{in}}$
\end{algorithmic}
| \begin{algorithmic}
\For{$\ell =0,\cdots,T_\text{out}-1$}
\For{$k=0,\cdots,T_\text{in}-1$} (concurrently for all $s\in\mathcal{S}$)
\State $\theta_{k+1}^{(i)} \gets (1-\eta\lambda)\theta_k^{(i)}-2\eta \nabla_{\theta,k}^{(i)}+\eta\widetilde{\nabla}_\theta^{(i)} +\sqrt{2\lambda\eta} \cdot\omega_k^{(i)}$, $\omega_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
\State $\phi_{k+1}^{(i)} \gets (1-\eta\lambda)\phi_k^{(i)}+2\eta \nabla_{\phi,k}^{(i)}-\eta\widetilde{\nabla}_\phi^{(i)} +\sqrt{2\lambda\eta} \cdot\beta_k^{(i)}$, $\beta_k^{(i)}\sim\mathcal{N}(0,\textbf{I})$
\State (computed with respect to the current action-value network $Q_\ell$)
\If{$k$ mod $K \equiv 0$}
\State $\widetilde{\nabla}_\theta^{(i)}, \widetilde{\nabla}_\phi^{(i)} \gets \nabla_{\theta,k}^{(i)}, \nabla_{\phi,k}^{(i)}$
\EndIf
\EndFor
\State perform some TD learning update $(Q_{\ell+1}(x,y|s))_{s\in\mathcal{S}}\gets (Q_\ell(x,y|s))_{s\in\mathcal{S}}$ using $\theta_{T_\text{in}}, \phi_{T_\text{in}}$
\EndFor
\Return $Q_{T_\text{out}}, \theta_{T_\text{in}}, \phi_{T_\text{in}}$
\end{algorithmic} | "https://arxiv.org/src/2312.01127" | "2312.01127.tar.gz" | "2024-02-16" | {
"title": "symmetric mean-field langevin dynamics for distributional minimax problems",
"id": "2312.01127",
"abstract": "in this paper, we extend mean-field langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. we propose mean-field langevin averaged gradient (mfl-ag), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed nash equilibrium. we also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. furthermore, we propose mean-field langevin anchored best response (mfl-abr), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. finally, we study applications to zero-sum markov games and conduct simulations demonstrating long-term optimality.",
"categories": "math.oc stat.ml",
"doi": "",
"created": "2023-12-02",
"updated": "2024-02-16",
"authors": [
"juno kim",
"kakei yamamoto",
"kazusato oko",
"zhuoran yang",
"taiji suzuki"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.01127"
} | "2024-03-15T05:16:00.811582" | {
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} | [] | "algorithm" | "e09a4ad9-8746-4e8c-a653-07fa6e89c508" | 1061 | medium |
|
\begin{algorithmic}
\State Pick uniformly at random a permutation $\pi$ over $[n]$.
\State For each $i \in [n]$ sample the $x_{i \pi(i)}$-coin. If any sample is $0$, restart.
\State Pick uniformly at random a spanning tree of the complete graph $K_n$.
\State Let $T$ be the set of edges $(i,j)$ of the tree oriented toward vertex $1$.
\State For each edge $(i,j) \in T$ sample the $x_{i \pi(j)}$-coin. If any sample is $0$, restart.
\State Output the matching $\{(i, \pi(i))\}_{i \in [n]}$.
\end{algorithmic}
| \begin{algorithmic}
\State Pick uniformly at random a permutation $\pi$ over $[n]$.
\State For each $i \in [n]$ sample the $x_{i \pi(i)}$-coin. If any sample is $0$, restart.
\State Pick uniformly at random a spanning tree of the complete graph $K_n$.
\State Let $T$ be the set of edges $(i,j)$ of the tree oriented toward vertex $1$.
\State For each edge $(i,j) \in T$ sample the $x_{i \pi(j)}$-coin. If any sample is $0$, restart.
\State Output the matching $\{(i, \pi(i))\}_{i \in [n]}$.
\end{algorithmic} | "https://arxiv.org/src/2011.03865" | "2011.03865.tar.gz" | "2024-02-19" | {
"title": "combinatorial bernoulli factories",
"id": "2011.03865",
"abstract": "a bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only bernoulli access to their parameters. bernoulli access to a parameter $p \\in [0,1]$ means the algorithm does not know $p$, but has sample access to independent draws of a bernoulli random variable with mean equal to $p$. in this paper, we study the problem of bernoulli factories for polytopes: given bernoulli access to a vector $x\\in p$ for a given polytope $p\\subset [0,1]^n$, output a randomized vertex such that the expected value of the $i$-th coordinate is \\emph{exactly} equal to $x_i$. for example, for the special case of the perfect matching polytope, one is given bernoulli access to the entries of a doubly stochastic matrix $[x_{ij}]$ and asked to sample a matching such that the probability of each edge $(i,j)$ be present in the matching is exactly equal to $x_{ij}$. we show that a polytope $p$ admits a bernoulli factory if and and only if $p$ is the intersection of $[0,1]^n$ with an affine subspace. our construction is based on an algebraic formulation of the problem, involving identifying a family of bernstein polynomials (one per vertex) that satisfy a certain algebraic identity on $p$. the main technical tool behind our construction is a connection between these polynomials and the geometry of zonotope tilings. we apply these results to construct an explicit factory for the perfect matching polytope. the resulting factory is deeply connected to the combinatorial enumeration of arborescences and may be of independent interest. for the $k$-uniform matroid polytope, we recover a sampling procedure known in statistics as sampford sampling.",
"categories": "cs.ds cs.dm cs.gt math.co math.pr",
"doi": "",
"created": "2020-11-07",
"updated": "2024-02-19",
"authors": [
"rad niazadeh",
"renato paes leme",
"jon schneider"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2011.03865"
} | "2024-03-15T04:22:53.719484" | {
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} | [] | "algorithm" | "ca7c0927-7aae-4fcd-809f-9f008b25aa4d" | 508 | easy |
|
\begin{algorithmic}[1]
\Procedure{CSP}{$m$, $n$, $D$, $B$, $F$}
\Comment{$D$: data register of size $m - n$}
\Comment{$B$: buffer register of size $\frac{N}{M} - 1$}
\Comment{$F$: flag register of size $\frac{N}{M} - 1$}
\For{$k$ \textbf{in} range($2^m$)}
\For{$s$ \textbf{in} range($n - m$) \textbf{and} $p$ \textbf{in} range($2^s$)}
\State Classically compute $\theta_{s,p}^{(k)}$ from $\mathbf{x}$ \Comment{Use Eq.~\eqref{eq:theta_ksp}}
\EndFor
\EndFor
\For{$s$ \textbf{in} range($n - m$) \textbf{and} $p$ \textbf{in} range($2^s$)}
\State $\mathrm{X}(F_{s,p})$ onto fresh ``flag'' ancilla
\EndFor
\State LOADF$(D, B, F)[\theta^{(k)}_{s,p}]$ load angles into buffer ancillae \Comment{$O(n)$}
\State SPF$(D, B, n-m)$ to prepare $n-m$ qubit state with garbage \Comment{$O(n-m)$}
\State FLAG$(D, F, n-m)$ \Comment{$O(n-m)$}
\State $\mathrm{LOADF}^{\dagger}$$(D, B, F)[\theta^{(k)}_{s,p}]$ to unload angles in buffer ancillae \Comment{$O(n)$}
\State $\mathrm{FLAG}^{\dagger}(D, F, n-m)$ \Comment{$O(n-m)$}
\For{$s$ \textbf{in} range($n - m$) \textbf{and} $p$ \textbf{in} range($2^s$)}
\State $\mathrm{X}(F_{s,p})$ to reset ``flag'' ancilla
\EndFor
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\Procedure{CSP}{$m$, $n$, $D$, $B$, $F$}
\Comment{$D$: data register of size $m - n$}
\Comment{$B$: buffer register of size $\frac{N}{M} - 1$}
\Comment{$F$: flag register of size $\frac{N}{M} - 1$}
\For{$k$ \textbf{in} range($2^m$)}
\For{$s$ \textbf{in} range($n - m$) \textbf{and} $p$ \textbf{in} range($2^s$)}
\State Classically compute $\theta_{s,p}^{(k)}$ from $\mathbf{x}$ \Comment{Use Eq.~\eqref{eq:theta_ksp}}
\EndFor
\EndFor
\For{$s$ \textbf{in} range($n - m$) \textbf{and} $p$ \textbf{in} range($2^s$)}
\State $\mathrm{X}(F_{s,p})$ onto fresh ``flag'' ancilla
\EndFor
\State LOADF$(D, B, F)[\theta^{(k)}_{s,p}]$ load angles into buffer ancillae \Comment{$O(n)$}
\State SPF$(D, B, n-m)$ to prepare $n-m$ qubit state with garbage \Comment{$O(n-m)$}
\State FLAG$(D, F, n-m)$ \Comment{$O(n-m)$}
\State $\mathrm{LOADF}^{\dagger}$$(D, B, F)[\theta^{(k)}_{s,p}]$ to unload angles in buffer ancillae \Comment{$O(n)$}
\State $\mathrm{FLAG}^{\dagger}(D, F, n-m)$ \Comment{$O(n-m)$}
\For{$s$ \textbf{in} range($n - m$) \textbf{and} $p$ \textbf{in} range($2^s$)}
\State $\mathrm{X}(F_{s,p})$ to reset ``flag'' ancilla
\EndFor
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2303.02131" | "2303.02131.tar.gz" | "2024-02-09" | {
"title": "spacetime-efficient low-depth quantum state preparation with applications",
"id": "2303.02131",
"abstract": "we propose a novel deterministic method for preparing arbitrary quantum states. when our protocol is compiled into cnot and arbitrary single-qubit gates, it prepares an $n$-dimensional state in depth $o(\\log(n))$ and spacetime allocation (a metric that accounts for the fact that oftentimes some ancilla qubits need not be active for the entire circuit) $o(n)$, which are both optimal. when compiled into the $\\{\\mathrm{h,s,t,cnot}\\}$ gate set, we show that it requires asymptotically fewer quantum resources than previous methods. specifically, it prepares an arbitrary state up to error $\\epsilon$ with optimal depth of $o(\\log(n) + \\log (1/\\epsilon))$ and spacetime allocation $o(n\\log(\\log(n)/\\epsilon))$, improving over $o(\\log(n)\\log(\\log (n)/\\epsilon))$ and $o(n\\log(n/\\epsilon))$, respectively. we illustrate how the reduced spacetime allocation of our protocol enables rapid preparation of many disjoint states with only constant-factor ancilla overhead -- $o(n)$ ancilla qubits are reused efficiently to prepare a product state of $w$ $n$-dimensional states in depth $o(w + \\log(n))$ rather than $o(w\\log(n))$, achieving effectively constant depth per state. we highlight several applications where this ability would be useful, including quantum machine learning, hamiltonian simulation, and solving linear systems of equations. we provide quantum circuit descriptions of our protocol, detailed pseudocode, and gate-level implementation examples using braket.",
"categories": "quant-ph cs.cc cs.lg",
"doi": "10.22331/q-2024-02-15-1257",
"created": "2023-03-03",
"updated": "2024-02-09",
"authors": [
"kaiwen gui",
"alexander m. dalzell",
"alessandro achille",
"martin suchara",
"frederic t. chong"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2303.02131"
} | "2024-03-15T03:55:47.804290" | {
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} | {
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} | [] | "algorithm" | "e6f610a7-349d-4692-b6d3-757b2d3fa6ff" | 1178 | hard |
|
\begin{algorithm}[ht]
\caption{Existence of a connected strongly-proportional allocation for $n$ agents.}
\label{alg:general}
\begin{algorithmic}[1]
\For{each permutation $\sigma : [n] \to [n]$}
\State \algorithmicif \ $\textsc{Mark}_{\sigma}(0, 1/n) < 1$ \algorithmicthen \ \Return true
\EndFor
\State \Return false
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[ht]
\caption{Existence of a connected strongly-proportional allocation for $n$ agents.}
\begin{algorithmic}
[1]
\For{each permutation $\sigma : [n] \to [n]$}
\State \algorithmicif \ $\textsc{Mark}_{\sigma}(0, 1/n) < 1$ \algorithmicthen \ \Return true
\EndFor
\State \Return false
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2312.15326" | "2312.15326.tar.gz" | "2024-02-13" | {
"title": "on connected strongly-proportional cake-cutting",
"id": "2312.15326",
"abstract": "we investigate the problem of fairly dividing a divisible heterogeneous resource, also known as a cake, among a set of agents. we characterize the existence of an allocation in which every agent receives a contiguous piece worth strictly more than their proportional share, also known as a *strongly-proportional allocation*. the characterization is supplemented with an algorithm that determines the existence of a connected strongly-proportional allocation using at most $n \\cdot 2^{n-1}$ queries. we provide a simpler characterization for agents with strictly positive valuations, and show that the number of queries required to determine the existence of a connected strongly-proportional allocation is in $\\theta(n^2)$. our proofs are constructive and yield a connected strongly-proportional allocation, when it exists, using a similar number of queries.",
"categories": "math.co cs.gt econ.th",
"doi": "",
"created": "2023-12-23",
"updated": "2024-02-13",
"authors": [
"zsuzsanna jank\u00f3",
"attila jo\u00f3",
"erel segal-halevi",
"sheung man yuen"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2312.15326"
} | "2024-03-15T04:11:23.042663" | {
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} | [] | "algorithm" | "ed521259-70a8-411f-93b9-d08074c75150" | 332 | easy |
|
\begin{algorithmic}[1]
\Require $\theta_0 \in \mathbb{R}^n, m \in (0, \infty)$
\State $z_0 = \theta_0, B_0 = 0, A_0 = 1/m$
\For{$t = 0,...$}
\State $B_{t+1} = B_t + .5(1+\sqrt{4B_t+1})$
\State $A_{t+1} = B_{t+1} + \frac{1}{m}$
\State $y_t = \theta_t + (1-\frac{A_t}{A_{t+1}})(z_t-\theta_t)$
\State $\theta_{t+1} = y_t - m\dot{F}(y_t)$
\State $z_{t+1} = z_t - m(A_{t+1}-A_t)\dot{F}(y_t)$
\EndFor
\end{algorithmic}
| \begin{algorithmic}
[1]
\Require $\theta_0 \in \mathbb{R}^n, m \in (0, \infty)$
\State $z_0 = \theta_0, B_0 = 0, A_0 = 1/m$
\For{$t = 0,...$}
\State $B_{t+1} = B_t + .5(1+\sqrt{4B_t+1})$
\State $A_{t+1} = B_{t+1} + \frac{1}{m}$
\State $y_t = \theta_t + (1-\frac{A_t}{A_{t+1}})(z_t-\theta_t)$
\State $\theta_{t+1} = y_t - m\dot{F}(y_t)$
\State $z_{t+1} = z_t - m(A_{t+1}-A_t)\dot{F}(y_t)$
\EndFor
\end{algorithmic} | "https://arxiv.org/src/2309.10894" | "2309.10894.tar.gz" | "2024-02-15" | {
"title": "a novel gradient methodology with economical objective function evaluations for data science applications",
"id": "2309.10894",
"abstract": "gradient methods are experiencing a growth in methodological and theoretical developments owing to the challenges of optimization problems arising in data science. focusing on data science applications with expensive objective function evaluations yet inexpensive gradient function evaluations, gradient methods that never make objective function evaluations are either being rejuvenated or actively developed. however, as we show, such gradient methods are all susceptible to catastrophic divergence under realistic conditions for data science applications. in light of this, gradient methods which make use of objective function evaluations become more appealing, yet, as we show, can result in an exponential increase in objective evaluations between accepted iterates. as a result, existing gradient methods are poorly suited to the needs of optimization problems arising from data science. in this work, we address this gap by developing a generic methodology that economically uses objective function evaluations in a problem-driven manner to prevent catastrophic divergence and avoid an explosion in objective evaluations between accepted iterates. our methodology allows for specific procedures that can make use of specific step size selection methodologies or search direction strategies, and we develop a novel step size selection methodology that is well-suited to data science applications. we show that a procedure resulting from our methodology is highly competitive with standard optimization methods on cutest test problems. we then show a procedure resulting from our methodology is highly favorable relative to standard optimization methods on optimization problems arising in our target data science applications. thus, we provide a novel gradient methodology that is better suited to optimization problems arising in data science.",
"categories": "math.oc stat.co",
"doi": "",
"created": "2023-09-19",
"updated": "2024-02-15",
"authors": [
"christian varner",
"vivak patel"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2309.10894"
} | "2024-03-15T05:06:27.333458" | {
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} | {
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} | [] | "algorithm" | "04c9daad-b238-4624-967b-f511e1706777" | 413 | easy |
|
\begin{algorithm}
\begin{algorithmic}
\Require{($\hat{x}_k,\hat{u}_k\,\hat{Q}_k,\hat{K}_k$)}
\For{$i=1\ldots N_{max}$}
\State{optimize $\bar{x}_k,\bar{u}_k$ by \eqref{eq:traj_update}}
\State{estimate $\gamma_k$ via \eqref{eq:gamma_update} or \eqref{eq:approximate_outer_optimization}}
\State{optimize $Q_k,K_k$ by \eqref{eq:funnel_update}}
\If{\eqref{eq:stopping_criterion} is True}
\State{break}
\EndIf
\State{update $(\hat{x}_k,\hat{u}_k\,\hat{Q}_k,\hat{K}_k)\leftarrow (\bar{x}_k,\bar{u}_k,Q_k,K_k)$}
\EndFor
\Ensure{$(\bar{x}_k,\bar{u}_k,Q_k,K_k)$}
\end{algorithmic}
\caption{Joint synthesis}
\label{alg:alg1}
\end{algorithm}
| \begin{algorithm}
\begin{algorithmic}
\Require{($\hat{x}_k,\hat{u}_k\,\hat{Q}_k,\hat{K}_k$)}
\For{$i=1\ldots N_{max}$}
\State{optimize $\bar{x}_k,\bar{u}_k$ by \eqref{eq:traj_update}}
\State{estimate $\gamma_k$ via \eqref{eq:gamma_update} or \eqref{eq:approximate_outer_optimization}}
\State{optimize $Q_k,K_k$ by \eqref{eq:funnel_update}}
\If{\eqref{eq:stopping_criterion} is True}
\State{break}
\EndIf
\State{update $(\hat{x}_k,\hat{u}_k\,\hat{Q}_k,\hat{K}_k)\leftarrow (\bar{x}_k,\bar{u}_k,Q_k,K_k)$}
\EndFor
\Ensure{$(\bar{x}_k,\bar{u}_k,Q_k,K_k)$}
\end{algorithmic}
\caption{Joint synthesis}
\end{algorithm} | "https://arxiv.org/src/2209.03535" | "2209.03535.tar.gz" | "2024-01-12" | {
"title": "joint synthesis of trajectory and controlled invariant funnel for discrete-time systems with locally lipschitz nonlinearities",
"id": "2209.03535",
"abstract": "this paper presents a joint synthesis algorithm of trajectory and controlled invariant funnel (cif) for locally lipschitz nonlinear systems subject to bounded disturbances. the cif synthesis refers to a procedure of computing controlled invariance sets and corresponding feedback gains. in contrast to existing cif synthesis methods that compute the cif with a pre-defined nominal trajectory, our work aims to optimize the nominal trajectory and the cif jointly to satisfy feasibility conditions without the relaxation of constraints and obtain a more cost-optimal nominal trajectory. the proposed work has a recursive scheme that mainly optimize trajectory update and funnel update. the trajectory update step optimizes the nominal trajectory while ensuring the feasibility of the cif. then, the funnel update step computes the funnel around the nominal trajectory so that the cif guarantees an invariance property. as a result, with the optimized trajectory and cif, any resulting trajectory propagated from an initial set by the control law with the computed feedback gain remains within the feasible region around the nominal trajectory under the presence of bounded disturbances. we validate the proposed method via two applications from robotics.",
"categories": "math.oc",
"doi": "",
"created": "2022-09-07",
"updated": "2024-01-12",
"authors": [
"taewan kim",
"purnanand elango",
"behcet acikmese"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2209.03535"
} | "2024-03-15T06:18:49.073482" | {
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} | [] | "algorithm" | "231c18d7-9786-4050-8973-c72e5d7b2ad8" | 612 | easy |
|
\begin{algorithm}[H]
\caption{{\sc Bernoulli Factory for $\P_{\alpha,n}$ for non-integer $\alpha$} (version 1)}
\label{alg:sampford_generic}
\begin{algorithmic}
\State Pick a random vertex $v$
\State For each index such that $v_i = 1$, sample the $x_i$-coin and restart if it is $0$.
\State For each index such that $v_i = 0$, sample the $x_i$-coin and restart if it is $1$.
\State For the remaining index $i$ sample two coins $x_i$-coins and restart unless their outcome is $0$ and $1$.
\State Output vertex $v$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\caption{{\sc Bernoulli Factory for $\P_{\alpha,n}$ for non-integer $\alpha$} (version 1)}
\begin{algorithmic}
\State Pick a random vertex $v$
\State For each index such that $v_i = 1$, sample the $x_i$-coin and restart if it is $0$.
\State For each index such that $v_i = 0$, sample the $x_i$-coin and restart if it is $1$.
\State For the remaining index $i$ sample two coins $x_i$-coins and restart unless their outcome is $0$ and $1$.
\State Output vertex $v$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2011.03865" | "2011.03865.tar.gz" | "2024-02-19" | {
"title": "combinatorial bernoulli factories",
"id": "2011.03865",
"abstract": "a bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only bernoulli access to their parameters. bernoulli access to a parameter $p \\in [0,1]$ means the algorithm does not know $p$, but has sample access to independent draws of a bernoulli random variable with mean equal to $p$. in this paper, we study the problem of bernoulli factories for polytopes: given bernoulli access to a vector $x\\in p$ for a given polytope $p\\subset [0,1]^n$, output a randomized vertex such that the expected value of the $i$-th coordinate is \\emph{exactly} equal to $x_i$. for example, for the special case of the perfect matching polytope, one is given bernoulli access to the entries of a doubly stochastic matrix $[x_{ij}]$ and asked to sample a matching such that the probability of each edge $(i,j)$ be present in the matching is exactly equal to $x_{ij}$. we show that a polytope $p$ admits a bernoulli factory if and and only if $p$ is the intersection of $[0,1]^n$ with an affine subspace. our construction is based on an algebraic formulation of the problem, involving identifying a family of bernstein polynomials (one per vertex) that satisfy a certain algebraic identity on $p$. the main technical tool behind our construction is a connection between these polynomials and the geometry of zonotope tilings. we apply these results to construct an explicit factory for the perfect matching polytope. the resulting factory is deeply connected to the combinatorial enumeration of arborescences and may be of independent interest. for the $k$-uniform matroid polytope, we recover a sampling procedure known in statistics as sampford sampling.",
"categories": "cs.ds cs.dm cs.gt math.co math.pr",
"doi": "",
"created": "2020-11-07",
"updated": "2024-02-19",
"authors": [
"rad niazadeh",
"renato paes leme",
"jon schneider"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2011.03865"
} | "2024-03-15T03:22:39.599567" | {
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} | [] | "algorithm" | "0d772c71-fcef-4b02-a6f9-a2ce5bdb3a9d" | 518 | easy |
|
\begin{algorithm}
\caption{Schematic outline of the steps required to obtain a mock galaxy catalogue with ScamPy.}
\begin{algorithmic}
\vspace{1mm}
\State{// \texttt{Load Halo/Subhalo hierarchy}}
\State{// \texttt{(e.g. from SUBFIND algorithm)}}
\State{halo\_cat = catalogue( \emph{ chosen from file } )}
\vspace{3mm}
\State{// \texttt{Choose occupation probability function}}
\State{OPF = OPF( \emph{HOD parameters} )}
\vspace{3mm}
\State{// \texttt{Populate haloes}}
\State{gxy\_array = halo\_cat.populate( model = OPF )}
\vspace{3mm}
\State{// \texttt{Associate luminosities}}
\State{gxy\_array = SHAM( gxy\_array, \emph{SHAM parameters} )}
\vspace{3mm}
\end{algorithmic}
\label{algo:populate}
\end{algorithm}
| \begin{algorithm}
\caption{Schematic outline of the steps required to obtain a mock galaxy catalogue with ScamPy.}
\begin{algorithmic}
\vspace{1mm}
\State{// \texttt{Load Halo/Subhalo hierarchy}}
\State{// \texttt{(e.g. from SUBFIND algorithm)}}
\State{halo\_cat = catalogue( \emph{ chosen from file } )}
\vspace{3mm}
\State{// \texttt{Choose occupation probability function}}
\State{OPF = OPF( \emph{HOD parameters} )}
\vspace{3mm}
\State{// \texttt{Populate haloes}}
\State{gxy\_array = halo\_cat.populate( model = OPF )}
\vspace{3mm}
\State{// \texttt{Associate luminosities}}
\State{gxy\_array = SHAM( gxy\_array, \emph{SHAM parameters} )}
\vspace{3mm}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2002.07179" | "2002.07179.tar.gz" | "2024-02-14" | {
"title": "scampy -- a sub-halo clustering & abundance matching based python interface for painting galaxies on the dark matter halo/sub-halo hierarchy",
"id": "2002.07179",
"abstract": "we present a computational framework for \"painting\" galaxies on top of the dark matter halo/sub-halo hierarchy obtained from n-body simulations. the method we use is based on the sub-halo clustering and abundance matching (scam) scheme which requires observations of the 1- and 2-point statistics of the target (observed) population we want to reproduce. this method is particularly tailored for high redshift studies and thereby relies on the observed high-redshift galaxy luminosity functions and correlation properties. the core functionalities are written in c++ and exploit object oriented programming, with a wide use of polymorphism, to achieve flexibility and high computational efficiency. in order to have an easily accessible interface, all the libraries are wrapped in python and provided with an extensive documentation. we validate our results and provide a simple and quantitative application to reionization, with an investigation of physical quantities related to the galaxy population, ionization fraction and bubble size distribution.",
"categories": "astro-ph.co",
"doi": "10.1093/mnras/staa2201",
"created": "2020-02-17",
"updated": "2024-02-14",
"authors": [
"tommaso ronconi",
"andrea lapi",
"matteo viel",
"alberto sartori"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2002.07179"
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} | [] | "algorithm" | "3192311a-2514-458b-af56-7f71784f7937" | 690 | easy |
|
\begin{algorithm}[H]
\centering
\caption{\textbf{-V.I:} Kernel CUSUM (KCUSUM)}\label{kcusumAlgo}
\begin{algorithmic}
\State \textbf{input:}Thresholds \(h\geq 0,\delta \ge \) and data \(x_1,x_2,\ldots\)
\State \textbf{initialize} \(Z_1=0\)
\State \textbf{For} \(n = 2,3,\ldots\)\textbf{do}
\State \hspace{3mm} \textbf{sample} \(y_n\) from reference measure \(p_o\)
\State \hspace{4mm} \textbf{if} \(n\) is even \textbf{then}
\State \hspace{5mm} \(v_n=g_\delta ((x_o,x_1),(y_o,y_1))\)
\State \hspace{3mm} \textbf{Else}
\State \hspace{5mm} \(v_n\)
\State \hspace{3mm} \textbf{end}
\State \hspace{3mm} \(Z_n = max\{0,Z_{n-1}+v_n\}\)
\State \hspace{3mm} \textbf{if} \(Z_n \ge h\),\textbf{then} set \(T_{KCUSUM}=n\) and \textbf{exit}
\State \hspace{3mm} \textbf{Else} continue
\State \textbf{end}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\centering
\caption{\textbf{-V.I:} Kernel CUSUM (KCUSUM)} \begin{algorithmic}
\State \textbf{input:}Thresholds \(h\geq 0,\delta \ge \) and data \(x_1,x_2,\ldots\)
\State \textbf{initialize} \(Z_1=0\)
\State \textbf{For} \(n = 2,3,\ldots\)\textbf{do}
\State \hspace{3mm} \textbf{sample} \(y_n\) from reference measure \(p_o\)
\State \hspace{4mm} \textbf{if} \(n\) is even \textbf{then}
\State \hspace{5mm} \(v_n=g_\delta ((x_o,x_1),(y_o,y_1))\)
\State \hspace{3mm} \textbf{Else}
\State \hspace{5mm} \(v_n\)
\State \hspace{3mm} \textbf{end}
\State \hspace{3mm} \(Z_n = max\{0,Z_{n-1}+v_n\}\)
\State \hspace{3mm} \textbf{if} \(Z_n \ge h\),\textbf{then} set \(T_{KCUSUM}=n\) and \textbf{exit}
\State \hspace{3mm} \textbf{Else} continue
\State \textbf{end}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2402.10291" | "2402.10291.tar.gz" | "2024-02-15" | {
"title": "an evaluation of real-time adaptive sampling change point detection algorithm using kcusum",
"id": "2402.10291",
"abstract": "detecting abrupt changes in real-time data streams from scientific simulations presents a challenging task, demanding the deployment of accurate and efficient algorithms. identifying change points in live data stream involves continuous scrutiny of incoming observations for deviations in their statistical characteristics, particularly in high-volume data scenarios. maintaining a balance between sudden change detection and minimizing false alarms is vital. many existing algorithms for this purpose rely on known probability distributions, limiting their feasibility. in this study, we introduce the kernel-based cumulative sum (kcusum) algorithm, a non-parametric extension of the traditional cumulative sum (cusum) method, which has gained prominence for its efficacy in online change point detection under less restrictive conditions. kcusum splits itself by comparing incoming samples directly with reference samples and computes a statistic grounded in the maximum mean discrepancy (mmd) non-parametric framework. this approach extends kcusum's pertinence to scenarios where only reference samples are available, such as atomic trajectories of proteins in vacuum, facilitating the detection of deviations from the reference sample without prior knowledge of the data's underlying distribution. furthermore, by harnessing mmd's inherent random-walk structure, we can theoretically analyze kcusum's performance across various use cases, including metrics like expected delay and mean runtime to false alarms. finally, we discuss real-world use cases from scientific simulations such as nwchem codar and protein folding data, demonstrating kcusum's practical effectiveness in online change point detection.",
"categories": "cs.lg stat.ml",
"doi": "",
"created": "2024-02-15",
"updated": "",
"authors": [
"vijayalakshmi saravanan",
"perry siehien",
"shinjae yoo",
"hubertus van dam",
"thomas flynn",
"christopher kelly",
"khaled z ibrahim"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.10291"
} | "2024-03-15T05:28:54.125577" | {
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|
\begin{algorithm}[H]
\footnotesize
\caption{\label{algorithm1}The instructions for the construction of the test statistics ${Q_m^t}$ and ${Q_m}$}
\hspace*{0.01in}
\begin{algorithmic}[1]
\State Construct the IV $z_{t-1}$ by equation (\ref{mulivz}).
\State Construct the IV estimators $\hat{\beta}_{ivx}$, $\hat{\beta}_a$ and $\hat{\beta}_b$ using the full sample and two subsamples by equations (\ref{defdeftwo2}), (\ref{muldef2new}) and (\ref{muldef3new}).
\State Eliminate the DE: Construct the weighted IV estimator $\hat{\beta}_l \equiv (W_1-W_2-W_3)^{-1}(W_1 \hat{\beta}_{ivx}-W_2\hat{\beta}_a -W_3 \hat{\beta}_b)$, where $W_1=\sum\nolimits_{t=1}^{T} \bar{z}_{t-1} x_{t-1}^\top $, $W_2=S_a \sum\nolimits_{t=1}^{T_0} \left( z_{t-1}- \frac{1}{T_0}\sum\nolimits_{t=1}^{T_0} z_{t-1} \right) x_{t-1}^\top$ and
$W_3=S_b \sum\nolimits_{t=T_0+1}^{T} \left( z_{t-1}- \frac{1}{T-T_0}\sum\nolimits_{t=T_0+1}^{T} z_{t-1} \right) x_{t-1}^\top$.
\State Control size for both SD and WD predictors:
\begin{itemize}
\item Reduce the DiE: Construct the estimator $\hat{\beta}_m = \hat{\beta}_{l}+ {B_m} {W_z} T^{-(1 -\delta) / 2} \frac{K+1}{2}{\hat{\rho}_{u v^*}}/ \sqrt{-2 c_z}$, where
${B_m}\equiv \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left( \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}\left(\operatorname{I_K}+ {W_z}\hat{\varpi}_l\hat{\varpi}_l^\top{W_z}^\top \right)^{1/2}$.
\item Reduce the VEE: Construct the estimator for the asymptotic covariance matrix of as $\operatorname{\widehat{Avar}}(\hat{\beta}_m ) \equiv H_l \left(\operatorname{I_K}+{W_z}\hat{\varpi}_l\hat{\varpi}_l^\top {W_z}^\top \right) H_l^\top$, where
$
H_l = \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left(\frac{T}{T-2K-1} \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}
$.
\item \textcolor{black}{Reduce the size distortion induced by the variance of the estimator of $u_t$: Use Lagrange-multiplier principle to obtain $\hat{u}_t= y_t - \hat{\mu}_s - x_{t-1}^\top \hat{\beta}_s$ by the constrained OLS estimation
$(\hat{\mu}_s,\hat{\beta}_s)^\top = \arg\, \min_{\mu,\beta} \left( y_t - \mu - x_{t-1}^\top \beta\right)^2,
\ s.t. \quad R\beta =r_J$.}
\end{itemize}
\State Construct the test statistic ${Q_m} \equiv \left(R \hat{\beta}_m -r_J \right)^\top \left[R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{-1} \left(R \hat{\beta}_m -r_J \right)$ with SD and WD predictors for $H_0:R\beta =r_J$.
\If{Focus on the one-sided marginal test $H_0:\beta_i=0$ vs $H_a:\beta_i>0$ and $H_0:\beta_i=0$ vs $H_a:\beta_i<0$ }
\State Construct the t-test statistic ${Q_m^t} \equiv \frac{R \hat{\beta}_m -r_J}{ \left[ R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{1/2}}$.
\EndIf
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
[H]
\footnotesize
\caption{The instructions for the construction of the test statistics ${Q_m^t}$ and ${Q_m}$}
\hspace*{0.01in}
\begin{algorithmic}
[1]
\State Construct the IV $z_{t-1}$ by equation (\ref{mulivz}).
\State Construct the IV estimators $\hat{\beta}_{ivx}$, $\hat{\beta}_a$ and $\hat{\beta}_b$ using the full sample and two subsamples by equations (\ref{defdeftwo2}), (\ref{muldef2new}) and (\ref{muldef3new}).
\State Eliminate the DE: Construct the weighted IV estimator $\hat{\beta}_l \equiv (W_1-W_2-W_3)^{-1}(W_1 \hat{\beta}_{ivx}-W_2\hat{\beta}_a -W_3 \hat{\beta}_b)$, where $W_1=\sum\nolimits_{t=1}^{T} \bar{z}_{t-1} x_{t-1}^\top $, $W_2=S_a \sum\nolimits_{t=1}^{T_0} \left( z_{t-1}- \frac{1}{T_0}\sum\nolimits_{t=1}^{T_0} z_{t-1} \right) x_{t-1}^\top$ and
$W_3=S_b \sum\nolimits_{t=T_0+1}^{T} \left( z_{t-1}- \frac{1}{T-T_0}\sum\nolimits_{t=T_0+1}^{T} z_{t-1} \right) x_{t-1}^\top$.
\State Control size for both SD and WD predictors:
\begin{itemize}
\item Reduce the DiE: Construct the estimator $\hat{\beta}_m = \hat{\beta}_{l}+ {B_m} {W_z} T^{-(1 -\delta) / 2} \frac{K+1}{2}{\hat{\rho}_{u v^*}}/ \sqrt{-2 c_z}$, where
${B_m}\equiv \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left( \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}\left(\operatorname{I_K}+ {W_z}\hat{\varpi}_l\hat{\varpi}_l^\top{W_z}^\top \right)^{1/2}$.
\item Reduce the VEE: Construct the estimator for the asymptotic covariance matrix of as $\operatorname{\widehat{Avar}}(\hat{\beta}_m ) \equiv H_l \left(\operatorname{I_K}+{W_z}\hat{\varpi}_l\hat{\varpi}_l^\top {W_z}^\top \right) H_l^\top$, where
$
H_l = \left( \sum_{t=1}^T \tilde{z}_{t-1} x_{t-1}^\top \right)^{-1}\left(\frac{T}{T-2K-1} \sum_{t=1}^T \tilde{z}_{t-1} \tilde{z}_{t-1}^\top \hat{u}_t^2 \right)^{1/2}
$.
\item \textcolor{black}{Reduce the size distortion induced by the variance of the estimator of $u_t$: Use Lagrange-multiplier principle to obtain $\hat{u}_t= y_t - \hat{\mu}_s - x_{t-1}^\top \hat{\beta}_s$ by the constrained OLS estimation
$(\hat{\mu}_s,\hat{\beta}_s)^\top = \arg\, \min_{\mu,\beta} \left( y_t - \mu - x_{t-1}^\top \beta\right)^2,
\ s.t. \quad R\beta =r_J$.}
\end{itemize}
\State Construct the test statistic ${Q_m} \equiv \left(R \hat{\beta}_m -r_J \right)^\top \left[R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{-1} \left(R \hat{\beta}_m -r_J \right)$ with SD and WD predictors for $H_0:R\beta =r_J$.
\If{Focus on the one-sided marginal test $H_0:\beta_i=0$ vs $H_a:\beta_i>0$ and $H_0:\beta_i=0$ vs $H_a:\beta_i<0$ }
\State Construct the t-test statistic ${Q_m^t} \equiv \frac{R \hat{\beta}_m -r_J}{ \left[ R\operatorname{\widehat{Avar}}(\hat{\beta}_m )R^\top\right]^{1/2}}$.
\EndIf
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2401.01064" | "2401.01064.tar.gz" | "2024-01-02" | {
"title": "robust inference for multiple predictive regressions with an application on bond risk premia",
"id": "2401.01064",
"abstract": "we propose a robust hypothesis testing procedure for the predictability of multiple predictors that could be highly persistent. our method improves the popular extended instrumental variable (ivx) testing (phillips and lee, 2013; kostakis et al., 2015) in that, besides addressing the two bias effects found in hosseinkouchack and demetrescu (2021), we find and deal with the variance-enlargement effect. we show that two types of higher-order terms induce these distortion effects in the test statistic, leading to significant over-rejection for one-sided tests and tests in multiple predictive regressions. our improved ivx-based test includes three steps to tackle all the issues above regarding finite sample bias and variance terms. thus, the test statistics perform well in size control, while its power performance is comparable with the original ivx. monte carlo simulations and an empirical study on the predictability of bond risk premia are provided to demonstrate the effectiveness of the newly proposed approach.",
"categories": "stat.me econ.em",
"doi": "",
"created": "2024-01-02",
"updated": "",
"authors": [
"xiaosai liao",
"xinjue li",
"qingliang fan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.01064"
} | "2024-03-15T06:49:14.014471" | {
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} | [] | "algorithm" | "fa60dee1-5185-4a5f-b279-eb310b9af968" | 2774 | hard |
|
\begin{algorithm}
\caption{Kalman filter algorithm}\label{euclidKF1}
\begin{algorithmic}[1]
\State Initialize with initial state $\Hat{X}_{(0)} = x_{(0)}$ and $\Hat{\boldsymbol{P}}_{(0)} = \boldsymbol{Q}^*$ at $t=0$;
\For {$t = 1,...,\textit{T}$}
\State $X_{(t)}^{t-1} = \boldsymbol{A}^* \Hat{X}_{(t-1)} + \boldsymbol{B}^* u_{(t)}$, \quad \text{State estimate extrapolation};
\State $\boldsymbol{P}_{(t)}^{t-1} = \boldsymbol{A}^* \Hat{\boldsymbol{P}}_{(t-1)}\boldsymbol{A}^{*'} + \boldsymbol{Q}^*$, \quad \text{State covariance extrapolation};
\State $\boldsymbol{K}_{(t)} = \boldsymbol{P}_{(t)}^{t-1} \boldsymbol{C}^{*'}[\boldsymbol{R}^* + \boldsymbol{C}^* \boldsymbol{P}_{(t)}^{t-1} \boldsymbol{C}^{*'}]^{-1}$, \quad \text{Kalman gain matrix};
\State $\Hat{X}_{(t)} = X_{(t)}^{t-1} + \boldsymbol{K}_{(t)} [Y_{(t)} - \boldsymbol{C}^* X_{(t)}^{t-1}]$, \quad \text{State estimate update};
\State $\Hat{\boldsymbol{P}}_{(t)} = [\boldsymbol{I} - \boldsymbol{K}_{(t)} \boldsymbol{C}^*] \boldsymbol{P}_{(t)}^{t-1} $, \quad \text{State covariance update};
\State Compute the log-likelihood contribution, $l_{(t)}^{\mathrm{KF}}$, at time $t$ through the density $\mbox{MVN}(Y_{(t)} - \boldsymbol{C}^* X_{(t)}^{t-1}, \boldsymbol{R}^* + \boldsymbol{C}^* \boldsymbol{P}_{(t)}^{t-1} \boldsymbol{C}^{*'})$;
\EndFor
\State The complete log-likelihood can be calculated as $L^* = \sum_t l_{(t)}^{\mathrm{KF}}$
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{Kalman filter algorithm}\begin{algorithmic}
[1]
\State Initialize with initial state $\Hat{X}_{(0)} = x_{(0)}$ and $\Hat{\boldsymbol{P}}_{(0)} = \boldsymbol{Q}^*$ at $t=0$;
\For {$t = 1,...,\textit{T}$}
\State $X_{(t)}^{t-1} = \boldsymbol{A}^* \Hat{X}_{(t-1)} + \boldsymbol{B}^* u_{(t)}$, \quad \text{State estimate extrapolation};
\State $\boldsymbol{P}_{(t)}^{t-1} = \boldsymbol{A}^* \Hat{\boldsymbol{P}}_{(t-1)}\boldsymbol{A}^{*'} + \boldsymbol{Q}^*$, \quad \text{State covariance extrapolation};
\State $\boldsymbol{K}_{(t)} = \boldsymbol{P}_{(t)}^{t-1} \boldsymbol{C}^{*'}[\boldsymbol{R}^* + \boldsymbol{C}^* \boldsymbol{P}_{(t)}^{t-1} \boldsymbol{C}^{*'}]^{-1}$, \quad \text{Kalman gain matrix};
\State $\Hat{X}_{(t)} = X_{(t)}^{t-1} + \boldsymbol{K}_{(t)} [Y_{(t)} - \boldsymbol{C}^* X_{(t)}^{t-1}]$, \quad \text{State estimate update};
\State $\Hat{\boldsymbol{P}}_{(t)} = [\boldsymbol{I} - \boldsymbol{K}_{(t)} \boldsymbol{C}^*] \boldsymbol{P}_{(t)}^{t-1} $, \quad \text{State covariance update};
\State Compute the log-likelihood contribution, $l_{(t)}^{\mathrm{KF}}$, at time $t$ through the density $\mbox{MVN}(Y_{(t)} - \boldsymbol{C}^* X_{(t)}^{t-1}, \boldsymbol{R}^* + \boldsymbol{C}^* \boldsymbol{P}_{(t)}^{t-1} \boldsymbol{C}^{*'})$;
\EndFor
\State The complete log-likelihood can be calculated as $L^* = \sum_t l_{(t)}^{\mathrm{KF}}$
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2105.04789" | "2105.04789.tar.gz" | "2024-02-10" | {
"title": "innovative approaches in soil carbon sequestration modelling for better prediction with limited data",
"id": "2105.04789",
"abstract": "soil carbon accounting and prediction play a key role in building decision support systems for land managers selling carbon credits, in the spirit of the paris and kyoto protocol agreements. land managers typically rely on computationally complex models fit using sparse datasets to make these accounts and predictions. the model complexity and sparsity of the data can lead to over-fitting, leading to inaccurate results when making predictions with new data. modellers address over-fitting by simplifying their models and reducing the number of parameters, and in the current context this could involve neglecting some soil organic carbon (soc) components. in this study, we introduce two novel soc models and a new rothc-like model and investigate how the soc components and complexity of the soc models affect the soc prediction in the presence of small and sparse time series data. we develop model selection methods that can identify the soil carbon model with the best predictive performance, in light of the available data. through this analysis we reveal that commonly used complex soil carbon models can over-fit in the presence of sparse time series data, and our simpler models can produce more accurate predictions. the published version of this study is available in scientific reports (https://www.nature.com/articles/s41598-024-53516-z/<10.1038/s41598-024-53516-z>)",
"categories": "stat.co stat.ap",
"doi": "10.1038/s41598-024-53516-z",
"created": "2021-05-11",
"updated": "2024-02-10",
"authors": [
"mohammad javad davoudabadi",
"daniel pagendam",
"christopher drovandi",
"jeff baldock",
"gentry white"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2105.04789"
} | "2024-03-15T06:18:35.682065" | {
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} | [] | "algorithm" | "b0dbd789-9d91-496d-8614-4a5ac3a491fe" | 1412 | hard |
|
\begin{algorithmic}[1]
\Procedure{penalizedG}{$\vec A, \vec H, \vec Y, \lambda$,\,corstr,\,$\kappa$} %Put comment if you want: \Comment{The g.c.d. of a and b}
\State Compute $E(\vec A_i|\vec H_i)$ for $i=1,\ldots,n$ \Comment{logistic regression on the pooled data}
\State $\vec\theta^{\text{up}} \gets \{\sum_{i=1}^n\vec D_i^\top(\vec H_i\;\;\vec A_i\cdot\vec H_i)\}^{-1}\sum_{i=1}^n\vec D_i^\top \vec Y_i$ \Comment{univariate unpenalized G-estimator}
\ForAll{$\lambda \in (\lambda_{max}, \ldots, \lambda_{min})$} %\Comment{We have the answer if r is 0}
\State Initialize: $t = 0$, $\vec\theta^0 \gets \vec\theta^{\text{up}}$
\Repeat
\State $\vec e_i \gets \vec Y_i - (\vec H_i\;\;\vec A_i\cdot\vec H_i)\vec\theta^t$ for $i=1,\ldots,n$%\Comment{comment}
\State Compute $\sigma^t$ and $\alpha^t$ under corstr using \ref{moment.method} \Comment{method of moments estimator}
\State Compute $\hat{\vec V}_i$ according to corstr for $i=1,\ldots,n$ \Comment{$\hat{\vec V}_i=\hat{\vec V}$ $\forall i$ if $J$ is fixed}
\State Compute $\vec S^{\text{eff}}(\vec\theta^t)$ using (\ref{form})
\State Compute $\vec H_n(\vec\theta^t)$ and $\vec E_n(\vec\theta^t)$ using (\ref{eq.Hn}) and (\ref{eq.En}), respectively.
\State Update $\vec\theta^{t}$ according to (\ref{update.penalizedG}) and obtain $\vec\theta^{t+1}$
\State $t \gets t+1$
\Until{$||\vec\theta^{t} - \vec\theta^{t-1}|| < \kappa$}\Comment{we set $\kappa=10^{-4}$}
\State $\tilde{\vec\theta}_\lambda \gets \vec\theta^t$, $\tilde{\sigma}_\lambda \gets \sigma^t$, and $\tilde{\alpha}_\lambda \gets \alpha^t$
\State Compute $\text{DRIC}_{\lambda}$ according to (\ref{dric})
\EndFor
\State $\tilde{\vec\theta} \gets \tilde{\vec\theta}_\lambda^*$ such that $\tilde{\vec\theta}_\lambda^*$ corresponds to the minimum of $\text{DRIC}_{\lambda}$
\State \textbf{return} $\tilde{\vec\theta}$
\EndProcedure
\end{algorithmic}
| \begin{algorithmic}
[1]
\Procedure{penalizedG}{$\vec A, \vec H, \vec Y, \lambda$,\,corstr,\,$\kappa$} %Put comment if you want: \Comment{The g.c.d. of a and b}
\State Compute $E(\vec A_i|\vec H_i)$ for $i=1,\ldots,n$ \Comment{logistic regression on the pooled data}
\State $\vec\theta^{\text{up}} \gets \{\sum_{i=1}^n\vec D_i^\top(\vec H_i\;\;\vec A_i\cdot\vec H_i)\}^{-1}\sum_{i=1}^n\vec D_i^\top \vec Y_i$ \Comment{univariate unpenalized G-estimator}
\ForAll{$\lambda \in (\lambda_{max}, \ldots, \lambda_{min})$} %\Comment{We have the answer if r is 0}
\State Initialize: $t = 0$, $\vec\theta^0 \gets \vec\theta^{\text{up}}$
\Repeat
\State $\vec e_i \gets \vec Y_i - (\vec H_i\;\;\vec A_i\cdot\vec H_i)\vec\theta^t$ for $i=1,\ldots,n$%\Comment{comment}
\State Compute $\sigma^t$ and $\alpha^t$ under corstr using \ref{moment.method} \Comment{method of moments estimator}
\State Compute $\hat{\vec V}_i$ according to corstr for $i=1,\ldots,n$ \Comment{$\hat{\vec V}_i=\hat{\vec V}$ $\forall i$ if $J$ is fixed}
\State Compute $\vec S^{\text{eff}}(\vec\theta^t)$ using (\ref{form})
\State Compute $\vec H_n(\vec\theta^t)$ and $\vec E_n(\vec\theta^t)$ using (\ref{eq.Hn}) and (\ref{eq.En}), respectively.
\State Update $\vec\theta^{t}$ according to (\ref{update.penalizedG}) and obtain $\vec\theta^{t+1}$
\State $t \gets t+1$
\Until{$||\vec\theta^{t} - \vec\theta^{t-1}|| < \kappa$}\Comment{we set $\kappa=10^{-4}$}
\State $\tilde{\vec\theta}_\lambda \gets \vec\theta^t$, $\tilde{\sigma}_\lambda \gets \sigma^t$, and $\tilde{\alpha}_\lambda \gets \alpha^t$
\State Compute $\text{DRIC}_{\lambda}$ according to (\ref{dric})
\EndFor
\State $\tilde{\vec\theta} \gets \tilde{\vec\theta}_\lambda^*$ such that $\tilde{\vec\theta}_\lambda^*$ corresponds to the minimum of $\text{DRIC}_{\lambda}$
\State \textbf{return} $\tilde{\vec\theta}$
\EndProcedure
\end{algorithmic} | "https://arxiv.org/src/2402.00154" | "2402.00154.tar.gz" | "2024-02-16" | {
"title": "penalized g-estimation for effect modifier selection in a structural nested mean model for repeated outcomes",
"id": "2402.00154",
"abstract": "effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. modeling of these effect differences is important for etiological goals and for purposes of optimizing treatment. structural nested mean models (snmms) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. a data-driven approach for selecting the effect modifiers of an exposure may be necessary if these effect modifiers are a priori unknown and need to be identified. although variable selection techniques are available in the context of estimating conditional average treatment effects using marginal structural models, or in the context of estimating optimal dynamic treatment regimens, all of these methods consider an outcome measured at a single point in time. in the context of an snmm for repeated outcomes, we propose a doubly robust penalized g-estimator for the causal effect of a time-varying exposure with a simultaneous selection of effect modifiers and use this estimator to analyze the effect modification in a study of hemodiafiltration. we prove the oracle property of our estimator, and conduct a simulation study for evaluation of its performance in finite samples and for verification of its double-robustness property. our work is motivated by and applied to the study of hemodiafiltration for treating patients with end-stage renal disease at the centre hospitalier de l'universit\\'e de montr\\'eal. we apply the proposed method to investigate the effect heterogeneity of dialysis facility on the repeated session-specific hemodiafiltration outcomes.",
"categories": "stat.me",
"doi": "",
"created": "2024-01-31",
"updated": "2024-02-16",
"authors": [
"ajmery jaman",
"guanbo wang",
"ashkan ertefaie",
"mich\u00e8le bally",
"ren\u00e9e l\u00e9vesque",
"robert w. platt",
"mireille e. schnitzer"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.00154"
} | "2024-03-15T05:18:15.887063" | {
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} | [] | "algorithm" | "53b6c355-7382-4f4e-8a61-656a6ce5f704" | 1862 | hard |
|
\begin{algorithm}[t]
\caption{Local structure-aware graph refinement in the $t$-th epoch}
\label{algorithm2}
\scriptsize
\begin{algorithmic}[1]
\Require $\mathcal{G} = (V, E) $, $\mathbf{H}^{(t-1)}=\left[\mathbf{h}_1^{(t-1)},\cdots \mathbf{h}_n^{(t-1)}\right]$, $\mathbf{A}^{(0)}$;
\Ensure $\mathbf{A}^{(t)}$;
\renewcommand{\algorithmicensure}{\textbf{Hyper-paramters:}}
\Ensure: $m$, $K$, $\gamma$
\State Initialization: $J_s = \phi$
\For{$u\in V$} /* \textit{Degree-based Node Sampling} */
\State $\mathbf{d}_u \leftarrow \sum_{v}^{|V|} \mathbf{A}^{(0)}_{u,v}$
\State $p_{s}(u) \leftarrow \frac{\mathbf{d}_u}{\sum_{i=1}^{n} \mathbf{d}_{i}}$
\EndFor
\For{$1$ to $m$}
\State Take a sampling on node $u_s$ from $V$ according to $p_{s}(u_s)$
\While{$v \in \tilde{\mathbf{N}}\left (u_s \right )$}
\State Calculate $\Delta_{u_{s},v} = \| \mathbf{h}_{u_s}^{(t-1)} - \mathbf{h}_{v}^{(t-1)} \|_2 $ %
\State $p_{s}(v) \leftarrow p_{s}(v) \cdot f(\Delta_{u_{s},v}) $
\EndWhile
\State $J_s \leftarrow J_s \cup \{u_s\}$
\EndFor
\While{sample node $u_s \in J_s$} /* \textit{Graph Refinement} */
\For{$k=1$ to $K$}
\State Select $\mathcal{k}$ nearest neighbors of $\mathbf{h}^{(t-1),k}_{u_s}$ as ${\mathbf{N}'}\left (u_s \right )$
\State $ \tilde{\mathbf{A}}^{(t-1),k}_{u_s,{\mathbf{N}'}\left (u_s \right )} \leftarrow \cos (\mathbf{h}^{(t-1),k}_{u_s}, \mathbf{h}^{(t-1),k}_{{\mathbf{N}'}\left (u_s \right )})$
\EndFor
\EndWhile
\State $\tilde{\mathbf{A}}^{(t-1)} \leftarrow \textrm{maxpooling}(\tilde{\mathbf{A}}^{(t-1),1},\tilde{\mathbf{A}}^{(t-1),2}, \cdots, \tilde{\mathbf{A}}^{(t-1),K})$
\State Obtain the refined $\mathbf{A}^{(t)}$ by Eq.(\ref{refining}).
\end{algorithmic}
\label{refinement}
\end{algorithm}
| \begin{algorithm}
[t]
\caption{Local structure-aware graph refinement in the $t$-th epoch}
\scriptsize
\begin{algorithmic}[1]
\Require $\mathcal{G} = (V, E) $, $\mathbf{H}^{(t-1)}=\left[\mathbf{h}_1^{(t-1)},\cdots \mathbf{h}_n^{(t-1)}\right]$, $\mathbf{A}^{(0)}$;
\Ensure $\mathbf{A}^{(t)}$;
\renewcommand{\algorithmicensure}{\textbf{Hyper-paramters:}}
\Ensure: $m$, $K$, $\gamma$
\State Initialization: $J_s = \phi$
\For{$u\in V$} /* \textit{Degree-based Node Sampling} */
\State $\mathbf{d}_u \leftarrow \sum_{v}^{|V|} \mathbf{A}^{(0)}_{u,v}$
\State $p_{s}(u) \leftarrow \frac{\mathbf{d}_u}{\sum_{i=1}^{n} \mathbf{d}_{i}}$
\EndFor
\For{$1$ to $m$}
\State Take a sampling on node $u_s$ from $V$ according to $p_{s}(u_s)$
\While{$v \in \tilde{\mathbf{N}}\left (u_s \right )$}
\State Calculate $\Delta_{u_{s},v} = \| \mathbf{h}_{u_s}^{(t-1)} - \mathbf{h}_{v}^{(t-1)} \|_2 $ %
\State $p_{s}(v) \leftarrow p_{s}(v) \cdot f(\Delta_{u_{s},v}) $
\EndWhile
\State $J_s \leftarrow J_s \cup \{u_s\}$
\EndFor
\While{sample node $u_s \in J_s$} /* \textit{Graph Refinement} */
\For{$k=1$ to $K$}
\State Select $\mathcal{k}$ nearest neighbors of $\mathbf{h}^{(t-1),k}_{u_s}$ as ${\mathbf{N}'}\left (u_s \right )$
\State $ \tilde{\mathbf{A}}^{(t-1),k}_{u_s,{\mathbf{N}'}\left (u_s \right )} \leftarrow \cos (\mathbf{h}^{(t-1),k}_{u_s}, \mathbf{h}^{(t-1),k}_{{\mathbf{N}'}\left (u_s \right )})$
\EndFor
\EndWhile
\State $\tilde{\mathbf{A}}^{(t-1)} \leftarrow \textrm{maxpooling}(\tilde{\mathbf{A}}^{(t-1),1},\tilde{\mathbf{A}}^{(t-1),2}, \cdots, \tilde{\mathbf{A}}^{(t-1),K})$
\State Obtain the refined $\mathbf{A}^{(t)}$ by Eq.(\ref{refining}).
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2103.07295" | "2103.07295.tar.gz" | "2024-01-24" | {
"title": "adversarial graph disentanglement",
"id": "2103.07295",
"abstract": "a real-world graph has a complex topological structure, which is often formed by the interaction of different latent factors. however, most existing methods lack consideration of the intrinsic differences in relations between nodes caused by factor entanglement. in this paper, we propose an \\underline{\\textbf{a}}dversarial \\underline{\\textbf{d}}isentangled \\underline{\\textbf{g}}raph \\underline{\\textbf{c}}onvolutional \\underline{\\textbf{n}}etwork (adgcn) for disentangled graph representation learning. to begin with, we point out two aspects of graph disentanglement that need to be considered, i.e., micro-disentanglement and macro-disentanglement. for them, a component-specific aggregation approach is proposed to achieve micro-disentanglement by inferring latent components that cause the links between nodes. on the basis of micro-disentanglement, we further propose a macro-disentanglement adversarial regularizer to improve the separability among component distributions, thus restricting the interdependence among components. additionally, to reveal the topological graph structure, a diversity-preserving node sampling approach is proposed, by which the graph structure can be progressively refined in a way of local structure awareness. the experimental results on various real-world graph data verify that our adgcn obtains more favorable performance over currently available alternatives. the source codes of adgcn are available at \\textit{\\url{https://github.com/ssgood/adgcn}}.",
"categories": "cs.lg cs.ai",
"doi": "",
"created": "2021-03-12",
"updated": "2024-01-24",
"authors": [
"shuai zheng",
"zhenfeng zhu",
"zhizhe liu",
"jian cheng",
"yao zhao"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2103.07295"
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} | [] | "algorithm" | "31ba0e21-4de4-48e4-bda1-4fd662693665" | 1664 | hard |
|
\begin{algorithm}
\label{fig: step_shrink}
A hybrid slice sampling transition of the stepping-out and shrinkage procedure from $x$ to $y$, i.e. input $x$ and output $y$.
The stepping-out procedure has input $x$ (current state), $t$ (chosen level),
$w>0$ (step size parameter from $\mathcal{R}_w$) and outputs an interval $[L,R]$.
The shrinkage procedure has input $[L,R]$ and output $y$:
\begin{enumerate}
\item Choose a level $t \sim \mathcal{U}(0,\rho(x))$;
\item Stepping-out with input $x,t,w$ outputs an interval $[L,R]$:
\begin{enumerate}
\item Choose $u \sim \mathcal{U}[0,1]$. Set $L=x-u w$ and $R=L+w$;
\item Repeat until $t \geq \rho(L)$, i.e. $L \not \in K(t)$: Set $L=L-w$;
\item Repeat until $t \geq \rho(R)$, i.e. $R \not \in K(t)$: Set $R=R+w$;
\end{enumerate}
\item Shrinkage procedure with input $[L,R]$ outputs $y$:
\begin{enumerate}
\item Set $\bar{L}=L$ and $\bar{R}=R$;
\item Repeat:
\begin{enumerate}
\item Choose $v\sim \mathcal{U}[0,1]$ and set $y=\bar{L}+ v (\bar{R}-\bar{L})$;
\item If $y \in K(t)$ then return $y$ and exit the loop;
\item If $y<x$ then set $\bar{L}=y$, else $\bar{R}=y$.
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{algorithm}
| \begin{algorithm}
A hybrid slice sampling transition of the stepping-out and shrinkage procedure from $x$ to $y$, i.e. input $x$ and output $y$.
The stepping-out procedure has input $x$ (current state), $t$ (chosen level),
$w>0$ (step size parameter from $\mathcal{R}_w$) and outputs an interval $[L,R]$.
The shrinkage procedure has input $[L,R]$ and output $y$:
\begin{enumerate}
\item Choose a level $t \sim \mathcal{U}(0,\rho(x))$;
\item Stepping-out with input $x,t,w$ outputs an interval $[L,R]$:
\begin{enumerate}
\item Choose $u \sim \mathcal{U}[0,1]$. Set $L=x-u w$ and $R=L+w$;
\item Repeat until $t \geq \rho(L)$, i.e. $L \not \in K(t)$: Set $L=L-w$;
\item Repeat until $t \geq \rho(R)$, i.e. $R \not \in K(t)$: Set $R=R+w$;
\end{enumerate}
\item Shrinkage procedure with input $[L,R]$ outputs $y$:
\begin{enumerate}
\item Set $\bar{L}=L$ and $\bar{R}=R$;
\item Repeat:
\begin{enumerate}
\item Choose $v\sim \mathcal{U}[0,1]$ and set $y=\bar{L}+ v (\bar{R}-\bar{L})$;
\item If $y \in K(t)$ then return $y$ and exit the loop;
\item If $y<x$ then set $\bar{L}=y$, else $\bar{R}=y$.
\end{enumerate}
\end{enumerate}
\end{enumerate}
\end{algorithm} | "https://arxiv.org/src/1409.2709" | "1409.2709.tar.gz" | "2024-02-09" | {
"title": "convergence of hybrid slice sampling via spectral gap",
"id": "1409.2709",
"abstract": "it is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. in contrast, we consider hybrid slice samplers which are easily implementable and where another markov chain approximately samples the uniform distribution on each slice. under appropriate assumptions on the markov chain on the slice we show a lower bound and an upper bound of the spectral gap of the hybrid slice sampler in terms of the spectral gap of the simple slice sampler. an immediate consequence of this is that spectral gap and geometric ergodicity of the hybrid slice sampler can be concluded from spectral gap and geometric ergodicity of its simple version which is very well understood. these results indicate that robustness properties of the simple slice sampler are inherited by (appropriately designed) easily implementable hybrid versions. we apply the developed theory and analyse a number of specific algorithms such as the stepping-out shrinkage slice sampling, hit-and-run slice sampling on a class of multivariate targets and an easily implementable combination of both procedures on multidimensional bimodal densities.",
"categories": "stat.me",
"doi": "",
"created": "2014-09-09",
"updated": "2024-02-09",
"authors": [
"krzysztof \u0142atuszy\u0144ski",
"daniel rudolf"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1409.2709"
} | "2024-03-15T06:20:58.276849" | {
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} | [] | "algorithm" | "42b76476-eeb3-4178-9697-30b2aae426d3" | 1153 | medium |
|
\begin{algorithm}
\caption{Generation of realizable degree sequence from a prescribed distribution}
\label{alg: Seq}
Consider size $N$ and the prescribed distribution given by $\mathbb{P}(D=d), d\in \mathbb{Z}_{>0}$
\begin{enumerate}
\item Following the algorithm described by \cite{Newman:2010}, we first draw a set of $N$ positive integer from the prescribed distribution.
\item If the sum of all $N$ integers in Step 1 is even, proceed the sequence to Step 3.
If there is an odd total Degree, randomly chose one of the vertices and changed its degree by drawing again from the prescribed distribution until the total number of stubs is even, then proceed to the next step.
\item Since both the order of vertices and the degree sequence have no impact when generating random graphs, we re-order and sort the sequence in descending order, as degree sequence $\textbf{d}$.
\item Check if the sequence $\textbf{d}$ satisfies Theorem~\ref{thm: Realizable}.
If satisfied, take $\textbf{d}$ as degree sequence.
Otherwise, restart from Step 1.
\end{enumerate}
\end{algorithm}
| \begin{algorithm}
\caption{Generation of realizable degree sequence from a prescribed distribution}
Consider size $N$ and the prescribed distribution given by $\mathbb{P}(D=d), d\in \mathbb{Z}_{>0}$
\begin{enumerate}
\item Following the algorithm described by \cite{Newman:2010}, we first draw a set of $N$ positive integer from the prescribed distribution.
\item If the sum of all $N$ integers in Step 1 is even, proceed the sequence to Step 3.
If there is an odd total Degree, randomly chose one of the vertices and changed its degree by drawing again from the prescribed distribution until the total number of stubs is even, then proceed to the next step.
\item Since both the order of vertices and the degree sequence have no impact when generating random graphs, we re-order and sort the sequence in descending order, as degree sequence $\textbf{d}$.
\item Check if the sequence $\textbf{d}$ satisfies Theorem~\ref{thm: Realizable}.
If satisfied, take $\textbf{d}$ as degree sequence.
Otherwise, restart from Step 1.
\end{enumerate}
\end{algorithm} | "https://arxiv.org/src/2401.06872" | "2401.06872.tar.gz" | "2024-01-12" | {
"title": "disease transmission on random graphs using edge-based percolation",
"id": "2401.06872",
"abstract": "edge-based percolation methods can be used to analyze disease transmission on complex social networks. this allows us to include complex social heterogeneity in our models while maintaining tractability. here we review the seminal works on this field by newman et al (2001); newman (2002, 2003), and miller et al (2012). we present a systematic discussion of the theoretical background behind these models, including an extensive derivation of the major results. we also connect these results relate back to the classical literature in random graph theory molloy and reed (1995, 1998). finally, we also present an accompanying r package that takes epidemic and network parameters as input and generates estimates of the epidemic trajectory and final size. this manuscript and the r package was developed to help researchers easily understand and use network models to investigate the interaction between different community structures and disease transmission.",
"categories": "cs.si math.ds q-bio.pe",
"doi": "",
"created": "2024-01-12",
"updated": "",
"authors": [
"s. zhao",
"f. m. g. magpantay"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.06872"
} | "2024-03-15T07:30:11.562367" | {
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} | [] | "algorithm" | "1737d0c0-567d-4d5b-b7be-2c69d1f38dbd" | 1053 | medium |
|
\begin{algorithm}[H]
\begin{algorithmic}
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Retrieve the values of $P_{u,t}$}
\State $P_{u,t}\leftarrow\textrm{{\tt Power.GetValue}}(t)$
\EndFor
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Initial conditions on the state variables}
\If{$P_{u,t} > \textrm{{\tt MinimumPower.GetValue}}(t)$}
\State $S_{u,t}^{OFF} \leftarrow 0$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\If{$P_{u,t} < P_{u,t-1}$}\Comment{Exact initialization required only if the FLAT state is defined.}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 1$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} > P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 1$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} = P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 1$
\EndIf
\ElsIf{$P_{u,t} > 0$}\Comment{Reconstruct the startups and shutdowns}
\If{$P_{u,t} < P_{u,t-1}$}
\State $S_{t}^{STOP} \leftarrow 1$
\State $S_{t}^{START} \leftarrow 0$
\Else
\State $S_{t}^{STOP} \leftarrow 0$
\State $S_{t}^{START} \leftarrow 1$
\EndIf
\Else\Comment{Final possibility: the unit is OFF.}
\State $S_{u,t}^{OFF} \leftarrow 1$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\EndIf
\EndFor
\end{algorithmic}
\caption{Initialization of the control and state variables}\label{alg:init_q_t_state_var}
\end{algorithm}
| \begin{algorithm}
[H]
\begin{algorithmic}
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Retrieve the values of $P_{u,t}$}
\State $P_{u,t}\leftarrow\textrm{{\tt Power.GetValue}}(t)$
\EndFor
\For{$t\in\{-1,\dots,-T^{traceback}\}$}\Comment{Initial conditions on the state variables}
\If{$P_{u,t} > \textrm{{\tt MinimumPower.GetValue}}(t)$}
\State $S_{u,t}^{OFF} \leftarrow 0$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\If{$P_{u,t} < P_{u,t-1}$}\Comment{Exact initialization required only if the FLAT state is defined.}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 1$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} > P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 1$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\ElsIf{$P_{u,t} = P_{u,t-1}$}
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 1$
\EndIf
\ElsIf{$P_{u,t} > 0$}\Comment{Reconstruct the startups and shutdowns}
\If{$P_{u,t} < P_{u,t-1}$}
\State $S_{t}^{STOP} \leftarrow 1$
\State $S_{t}^{START} \leftarrow 0$
\Else
\State $S_{t}^{STOP} \leftarrow 0$
\State $S_{t}^{START} \leftarrow 1$
\EndIf
\Else\Comment{Final possibility: the unit is OFF.}
\State $S_{u,t}^{OFF} \leftarrow 1$
\State $S_{u,t}^{STOP} \leftarrow 0$
\State $S_{u,t}^{START} \leftarrow 0$
\State $S_{t-1}^{ON\_UP} \leftarrow 0$
\State $S_{t-1}^{ON\_DOWN} \leftarrow 0$
\State $S_{t-1}^{ON\_FLAT} \leftarrow 0$
\EndIf
\EndFor
\end{algorithmic}
\caption{Initialization of the control and state variables}\end{algorithm} | "https://arxiv.org/src/2402.12848" | "2402.12848.tar.gz" | "2024-02-20" | {
"title": "atlas: a model of short-term european electricity market processes under uncertainty",
"id": "2402.12848",
"abstract": "the atlas model simulates the various stages of the electricity market chain in europe, including the formulation of offers by different market actors, the coupling of european markets, strategic optimization of production portfolios and, finally, real-time system balancing processes. atlas was designed to simulate the various electricity markets and processes that occur from the day ahead timeframe to real-time with a high level of detail. its main aim is to capture impacts from imperfect actor coordination, evolving forecast errors and a high-level of technical constraints--both regarding different production units and the different market constraints.",
"categories": "econ.gn math.oc q-fin.ec",
"doi": "",
"created": "2024-02-20",
"updated": "",
"authors": [
"emily little",
"florent cogen",
"quentin bustarret",
"virginie dussartre",
"maxime l\u00e2asri",
"gabriel kasmi",
"marie girod",
"frederic bienvenu",
"maxime fortin",
"jean-yves bourmaud"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2402.12848"
} | "2024-03-15T03:38:34.361656" | {
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} | [] | "algorithm" | "e51006a5-6848-4672-acd2-96726cd529b0" | 1623 | hard |
|
\begin{algorithm}[t] % enter the algorithm environment
\caption{Independent Metropolis-Hastings (IMH) Algorithm} % give the algorithm a caption
\label{alg1} % and a label for \ref{} commands later in the document
\begin{algorithmic} % enter the algorithmic environment
\State Pick an initial state $(x_0,y_0,z_0) \sim \nu(x,y,z)$.
\For{$i = 0, 1, 2, \dots$}
\State Generate a random candidate state $(x', y', z') \sim \nu(x,y,z)$.
\State Calculate the acceptance probability $A(x_i, y_i, z_i, x', y', z') = \min\left\{1, \frac{\pi(x',y',z')\nu(x_i,y_i,z_i)}{\pi(x_i,y_i,z_i)\nu(x',y',z')}\right\}$
\State Generate a uniform random number $u \in [0,1]$.
\If{$u \le A(x_i,y_i,z_i, x', y', z')$}
\State accept the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x',y',z')$.
\Else
\State reject the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x_i, y_i, z_i)$.
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}[t]
% enter the algorithm environment
\caption{Independent Metropolis-Hastings (IMH) Algorithm} % give the algorithm a caption
% and a label for \ref{} commands later in the document
\begin{algorithmic}
% enter the algorithmic environment
\State Pick an initial state $(x_0,y_0,z_0) \sim \nu(x,y,z)$.
\For{$i = 0, 1, 2, \dots$}
\State Generate a random candidate state $(x', y', z') \sim \nu(x,y,z)$.
\State Calculate the acceptance probability $A(x_i, y_i, z_i, x', y', z') = \min\left\{1, \frac{\pi(x',y',z')\nu(x_i,y_i,z_i)}{\pi(x_i,y_i,z_i)\nu(x',y',z')}\right\}$
\State Generate a uniform random number $u \in [0,1]$.
\If{$u \le A(x_i,y_i,z_i, x', y', z')$}
\State accept the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x',y',z')$.
\Else
\State reject the new state $(x',y',z')$ and set $(x_{i+1}, y_{i+1}, z_{i+1}) = (x_i, y_i, z_i)$.
\EndIf
\EndFor
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/1805.10721" | "1805.10721.tar.gz" | "2024-01-11" | {
"title": "bernstein's inequalities for general markov chains",
"id": "1805.10721",
"abstract": "we establish bernstein's inequalities for functions of general (general-state-space and possibly non-reversible) markov chains. these inequalities achieve sharp variance proxies and encompass the classical bernstein inequality for independent random variables as special cases. the key analysis lies in bounding the operator norm of a perturbed markov transition kernel by the exponential of sum of two convex functions. one coincides with what delivers the classical bernstein inequality, and the other reflects the influence of the markov dependence. a convex analysis on these two functions then derives our bernstein inequalities. as applications, we apply our bernstein inequalities to the markov chain monte carlo integral estimation problem and the robust mean estimation problem with markov-dependent samples, and achieve tight deviation bounds that previous inequalities can not.",
"categories": "math.st stat.th",
"doi": "",
"created": "2018-05-27",
"updated": "2024-01-11",
"authors": [
"bai jiang",
"qiang sun",
"jianqing fan"
],
"affiliation": [],
"url": "https://arxiv.org/abs/1805.10721"
} | "2024-03-15T06:32:05.168692" | {
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} | [] | "algorithm" | "a48f11a3-ada8-42d2-bcd3-c2a00e6baa12" | 925 | medium |
|
\begin{algorithmic}[1]
\Function {makeGraph}{$reads$}
\ForAll{$r$ in $reads$}
\ForAll{$kmer$ in $r$}
\State $left \gets s_{0}s_{1}\dots{}s_{k-2}$ //prefix
\State $right \gets s_{1}\dots{}s_{k-2}s_{k-1}$ //suffix
\State $addLeftVertex(left, s_{k-1})$
\State $addRightVertex(right)$
\State {// now both left and right vertex exist}
\State $left\_vertex \gets FindVertex(left)$
\State $right\_vertex \gets FindVertex(right)$
\State $left\_vertex.pointers[s_{k-1}] \gets right\_vertex$
\EndFor
\EndFor
\EndFunction
\end{algorithmic}
| \begin{algorithmic}
[1]
\Function {makeGraph}{$reads$}
\ForAll{$r$ in $reads$}
\ForAll{$kmer$ in $r$}
\State $left \gets s_{0}s_{1}\dots{}s_{k-2}$ //prefix
\State $right \gets s_{1}\dots{}s_{k-2}s_{k-1}$ //suffix
\State $addLeftVertex(left, s_{k-1})$
\State $addRightVertex(right)$
\State {// now both left and right vertex exist}
\State $left\_vertex \gets FindVertex(left)$
\State $right\_vertex \gets FindVertex(right)$
\State $left\_vertex.pointers[s_{k-1}] \gets right\_vertex$
\EndFor
\EndFor
\EndFunction
\end{algorithmic} | "https://arxiv.org/src/2401.02756" | "2401.02756.tar.gz" | "2024-01-05" | {
"title": "lock-free de bruijn graph",
"id": "2401.02756",
"abstract": "de bruijn graph is one of the most important data structures used in de-novo genome assembly algorithms, especially for ngs data. there is a growing need for parallel data structures and algorithms due to the increasing number of cores in modern computers. the assembly task is an indispensable step in sequencing genomes of new organisms and studying structural genomic changes. in recent years, the dynamic development of next-generation sequencing (ngs) methods raises hopes for making whole-genome sequencing a fast and reliable tool used, for example, in medical diagnostics. however, this is hampered by the slowness and computational requirements of the current processing algorithms, which raises the need to develop more efficient algorithms. one possible approach, still little explored, is the use of quantum computing. we created the lock-free version of the de bruijn graph, as well as a lock-free algorithm to build such graph from reads. our algorithm and data structures are developed to use parallel threads of execution and do not use mutexes or other locking mechanisms, instead, we used only compare-and-swap instruction and other atomic operations. it makes our algorithm very fast and efficiently scaling. the presented article depicts the new lock-free de bruijn graph data structure with a graph build algorithm. we developed a c++ library and tested its performance to depict its high speed and scalability compared to other available tools.",
"categories": "cs.dc q-bio.gn",
"doi": "",
"created": "2024-01-05",
"updated": "",
"authors": [
"daniel g\u00f3rniak",
"robert nowak"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2401.02756"
} | "2024-03-15T07:57:44.023666" | {
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} | [] | "algorithm" | "69d6fd6f-05c1-4ab0-89b7-a3a067759544" | 529 | easy |
|
\begin{algorithmic}[1]
\State \textbf{Input:} initial point $w_0$, learning rate $\eta$, preconditioner $\hat{D}_0$, probability $p$
\State $v_0 = \nabla P(w_0)$ \label{SARAHbegin}
\For{$t = 0,1,2,\ldots$}
\State $w_{t+1} = w_t - \eta \hat{D}^{-1}_{t}v_t$\label{SARAHpreconditionedstep}
\State Generate independently batches $i_{t+1}$ for $v_{t+1}$ and $\mathcal{J}_t$ for $\hat{D}_{t+1}$
\State $v_{t+1} = \begin{cases}
\nabla P(w_{t+1}), & \text{with probability } p
\\
v_{t} + \nabla f_{i_{t+1}}(w_{t+1}) - \nabla f_{i_{t+1}}(w_t), & \text{with probability } 1 - p
\end{cases}$\label{SARAHupdate}
\State Update the preconditioner $\hat{D}_{t+1}$ %according to \eqref{approx_Hessian_1},\eqref{approx_Hessian_2}
\EndFor
\State \textbf{Output:} $\hat{w}_T$ chosen uniformly from $\{w_t\}^T_{t=0}$
\end{algorithmic}
| \begin{algorithmic}
[1]
\State \textbf{Input:} initial point $w_0$, learning rate $\eta$, preconditioner $\hat{D}_0$, probability $p$
\State $v_0 = \nabla P(w_0)$ \For{$t = 0,1,2,\ldots$}
\State $w_{t+1} = w_t - \eta \hat{D}^{-1}_{t}v_t$ \State Generate independently batches $i_{t+1}$ for $v_{t+1}$ and $\mathcal{J}_t$ for $\hat{D}_{t+1}$
\State $v_{t+1} = \begin{cases}
\nabla P(w_{t+1}), & \text{with probability } p
\\
v_{t} + \nabla f_{i_{t+1}}(w_{t+1}) - \nabla f_{i_{t+1}}(w_t), & \text{with probability } 1 - p
\end{cases}$ \State Update the preconditioner $\hat{D}_{t+1}$ %according to \eqref{approx_Hessian_1},\eqref{approx_Hessian_2}
\EndFor
\State \textbf{Output:} $\hat{w}_T$ chosen uniformly from $\{w_t\}^T_{t=0}$
\end{algorithmic} | "https://arxiv.org/src/2206.00285" | "2206.00285.tar.gz" | "2024-01-14" | {
"title": "stochastic gradient methods with preconditioned updates",
"id": "2206.00285",
"abstract": "this work considers the non-convex finite sum minimization problem. there are several algorithms for such problems, but existing methods often work poorly when the problem is badly scaled and/or ill-conditioned, and a primary goal of this work is to introduce methods that alleviate this issue. thus, here we include a preconditioner based on hutchinson's approach to approximating the diagonal of the hessian, and couple it with several gradient-based methods to give new scaled algorithms: scaled sarah and scaled l-svrg. theoretical complexity guarantees under smoothness assumptions are presented. we prove linear convergence when both smoothness and the pl condition are assumed. our adaptively scaled methods use approximate partial second-order curvature information and, therefore, can better mitigate the impact of badly scaled problems. this improved practical performance is demonstrated in the numerical experiments also presented in this work.",
"categories": "math.oc cs.lg",
"doi": "",
"created": "2022-06-01",
"updated": "2024-01-14",
"authors": [
"abdurakhmon sadiev",
"aleksandr beznosikov",
"abdulla jasem almansoori",
"dmitry kamzolov",
"rachael tappenden",
"martin tak\u00e1\u010d"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2206.00285"
} | "2024-03-15T06:13:46.815677" | {
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} | [] | "algorithm" | "ca38e228-41f8-4053-831c-8c671d72d632" | 750 | medium |
|
\begin{algorithm}
\caption{The Queue Shuffle } \label{algo:qs}
\begin{algorithmic}[1]
\Require $\mathcal{T}$ \Comment{Current Tree}
\Require $\mathcal{N} = \{\nu_0,\nu_1,...\}$ \Comment{set of all non-root nodes}
\State $Q = [\nu_0,\nu_1]$ \Comment{"queue" of nodes to process}
\State $L = \{\nu_0 : 0, \nu_1 : 1\}$ \Comment{node:label mapping}
\State $l_{\text{next}} = 2$\Comment{next available label}
\State $P = []$ \Comment{processed nodes}
\While{$Q \neq []$}
\State $\nu = Q[0]$ \Comment{node to process}
\State Q = Q[1:] \Comment{$\nu$ will be processed}
\State $\text{append}(P,\nu)$ \Comment{$\nu$ will be processed}
\If{$\text{isLeaf}(\nu)$}
\State \textbf{continue} \Comment{move to next node}
\EndIf
\State $a,b = \text{randChildren}(\nu)$ \Comment{get \textbf{randomly ordered} children of $\nu$}
\State $L[a] = L[\nu]$ \Comment{label $a$ with $\nu$'s label}
\State $L[b] = l_{\text{next}}$ \Comment{give $b$ next available label}
\State $l_{\text{next}} = l_{\text{next}} +1$
\State append($Q,a$) \Comment{add $a$ to the queue}
\State append$(Q,b)$ \Comment{add $b$ to the queue}
\EndWhile
\State \text{{Return }} $L$ \Comment{Ordering determined by values of $L$ for leaf nodes}
\end{algorithmic}
\end{algorithm}
| \begin{algorithm}
\caption{The Queue Shuffle } \begin{algorithmic}
[1]
\Require $\mathcal{T}$ \Comment{Current Tree}
\Require $\mathcal{N} = \{\nu_0,\nu_1,...\}$ \Comment{set of all non-root nodes}
\State $Q = [\nu_0,\nu_1]$ \Comment{"queue" of nodes to process}
\State $L = \{\nu_0 : 0, \nu_1 : 1\}$ \Comment{node:label mapping}
\State $l_{\text{next}} = 2$\Comment{next available label}
\State $P = []$ \Comment{processed nodes}
\While{$Q \neq []$}
\State $\nu = Q[0]$ \Comment{node to process}
\State Q = Q[1:] \Comment{$\nu$ will be processed}
\State $\text{append}(P,\nu)$ \Comment{$\nu$ will be processed}
\If{$\text{isLeaf}(\nu)$}
\State \textbf{continue} \Comment{move to next node}
\EndIf
\State $a,b = \text{randChildren}(\nu)$ \Comment{get \textbf{randomly ordered} children of $\nu$}
\State $L[a] = L[\nu]$ \Comment{label $a$ with $\nu$'s label}
\State $L[b] = l_{\text{next}}$ \Comment{give $b$ next available label}
\State $l_{\text{next}} = l_{\text{next}} +1$
\State append($Q,a$) \Comment{add $a$ to the queue}
\State append$(Q,b)$ \Comment{add $b$ to the queue}
\EndWhile
\State \text{{Return }} $L$ \Comment{Ordering determined by values of $L$ for leaf nodes}
\end{algorithmic}
\end{algorithm} | "https://arxiv.org/src/2306.05739" | "2306.05739.tar.gz" | "2024-01-23" | {
"title": "leaping through tree space: continuous phylogenetic inference for rooted and unrooted trees",
"id": "2306.05739",
"abstract": "phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. however, finding suitable phylogenies from the vast space of possible trees remains challenging. to address this problem, for the first time, we perform both tree exploration and inference in a continuous space where the computation of gradients is possible. this continuous relaxation allows for major leaps across tree space in both rooted and unrooted trees, and is less susceptible to convergence to local minima. our approach outperforms the current best methods for inference on unrooted trees and, in simulation, accurately infers the tree and root in ultrametric cases. the approach is effective in cases of empirical data with negligible amounts of data, which we demonstrate on the phylogeny of jawed vertebrates. indeed, only a few genes with an ultrametric signal were generally sufficient for resolving the major lineages of vertebrates. optimisation is possible via automatic differentiation and our method presents an effective way forwards for exploring the most difficult, data-deficient phylogenetic questions.",
"categories": "q-bio.pe cs.lg",
"doi": "10.1093/gbe/evad213",
"created": "2023-06-09",
"updated": "2024-01-23",
"authors": [
"matthew j penn",
"neil scheidwasser",
"joseph penn",
"christl a donnelly",
"david a duch\u00eane",
"samir bhatt"
],
"affiliation": [],
"url": "https://arxiv.org/abs/2306.05739"
} | "2024-03-15T06:52:58.742216" | {
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