:tada: initial commit

app.py

@@ -0,0 +1,126 @@
+import streamlit as st
+import plotly.graph_objects as go
+import numpy as np
+import scipy.integrate as integrate
+
+def _false_positive_probability(threshold, b, r):
+    def _probability(s):
+        return 1 - (1 - s ** float(r)) ** float(b)
+    a, err = integrate.quad(_probability, 0.0, threshold)
+    return a
+
+
+def _false_negative_probability(threshold, b, r):
+    def _probability(s):
+        return 1 - (1 - (1 - s ** float(r)) ** float(b))
+
+    a, err = integrate.quad(_probability, threshold, 1.0)
+    return a
+
+
+def _optimal_param(threshold, num_perm, false_positive_weight, false_negative_weight):
+    """
+    Compute the optimal `MinHashLSH` parameter that minimizes the weighted sum
+    of probabilities of false positive and false negative.
+    """
+    min_error = float("inf")
+    opt = (0, 0)
+    for b in range(1, num_perm + 1):
+        max_r = int(num_perm / b)
+        for r in range(1, max_r + 1):
+            fp = _false_positive_probability(threshold, b, r)
+            fn = _false_negative_probability(threshold, b, r)
+            error = fp * false_positive_weight + fn * false_negative_weight
+            if error < min_error:
+                min_error = error
+                opt = (b, r)
+    return opt
+
+
+col1, col2 = st.columns(2)
+s = col1.slider("Select a Jaccard similarity", 0.0, 1.0, 0.1)
+p = col2.slider("Select a number of permutations", 0, 1000, 10)
+optimal_b, optimal_r = _optimal_param(s, p, 1, 1)
+
+b = col1.slider("Select a number of bands", 1, 100, 1)
+r = col2.slider("Select a number of rows per band", 1, 100, 1)
+
+col1.metric(label="Optimal number of bands", value=optimal_b)
+col2.metric(label="Optimal number of rows per band", value=optimal_r)
+
+st.markdown("---")
+
+st.markdown(f"Two documents that have a Jaccard similarity of $s={s}$ will have:")
+st.markdown(f"1. ${s * 100:.2f}\%$ of their k-shingles will be the same")
+st.markdown(f"2. ${s * 100:.2f}\%$ of their k-shingles' hashes will be the same")
+st.markdown(f"4. ${s * 100:.2f}\%$ of the time, a particular hash will be the same for two documents")
+st.markdown(
+    f"3. $s^r={100 * s ** r:.2f}\%$ of the time, they will have the same hashes for a particular band of $r={r}$ rows"
+)
+st.markdown(
+    f"5. $1 - s^r = {100 * (1 - s ** r):.2f}\%$ of the time, they will have at least one different hash for a particular band"
+)
+st.markdown(
+    f"6. $(1 - s^r)^b = {100 * (1 - s ** r)**b:.2f}\%$ of the time, they will have at least one different hash for all $b={b}$ bands"
+)
+st.markdown(
+    f"7. $1 - (1 - s^r)^b={100 * (1 - (1 - s ** r)**b):.2f}\%$ of the time, they will have at least one band with the same hashes"
+)
+
+t = st.slider("Select a Jaccard similarity threshold", 0.0, 1.0, 0.1)
+
+x = np.linspace(0, 1, 1000)
+y = 1 - (1 - x**r) ** b
+
+fig = go.Figure(
+    data=go.Scatter(
+        x=x,
+        y=y,
+        showlegend=False,
+    )
+)
+fig = fig.add_shape(
+    type="line",
+    x0=t,
+    y0=0,
+    x1=t,
+    y1=1,
+    line=dict(
+        color="Red",
+        width=4,
+    ),
+)
+false_positive_x = [d for d in x if d <= t] + [t]
+false_positive_y = [d for i, d in enumerate(y) if x[i] <= t] + [0]
+fig.add_trace(
+    go.Scatter(
+        x=false_positive_x,
+        y=false_positive_y,
+        fill="tozeroy",
+        fillcolor="rgba(255, 0, 0, 0.2)",
+        line_color="rgba(255, 0, 0, 0)",
+        showlegend=False,
+    )
+)
+
+false_negative_x = [d for d in x if d > t]
+false_negative_y = [d for i, d in enumerate(y) if x[i] > t]
+fig.add_trace(
+    go.Scatter(
+        x=[t] + false_negative_x + [1],
+        y=[1] + false_negative_y + [1],
+        fill="toself",
+        fillcolor="rgba(0, 255, 0, 0.2)",
+        line_color="rgba(0, 255, 0, 0)",
+        showlegend=False,
+    )
+)
+
+st.plotly_chart(fig)
+
+false_positive = integrate.quad(lambda x: 1 - (1 - x**r) ** b, 0, t)[0]
+false_negative = integrate.quad(lambda x: (1 - x**r) ** b, t, 1)[0]
+
+cols = st.columns(2)
+cols[0].metric(label="False positive area", value=f"{false_positive:.2f}")
+cols[1].metric(label="False negative area", value=f"{false_negative:.2f}")