Comparing distributions¶

Hypergrid provides four divergence metrics for comparing two grids:

Method	Description	Symmetric
l1	Total variation distance	Yes
js	Jensen-Shannon divergence, bounded in [0, 1]	Yes
kl	Kullback-Leibler divergence	No
wasserstein	Earth Mover's Distance via LP	Yes

In [1]:

import numpy as np
import matplotlib.pyplot as plt

from hypergrid import DenseHypergrid, compute_edges

import numpy as np import matplotlib.pyplot as plt from hypergrid import DenseHypergrid, compute_edges

1. Two identical distributions → divergence should be 0¶

In [2]:

rng = np.random.default_rng(0)
data = rng.standard_normal((3000, 2))
edges = compute_edges(data)

g1 = DenseHypergrid(edges)
g2 = DenseHypergrid(edges)
g1.fit(data)
g2.fit(data)

for method in ["l1", "js", "kl"]:
    print(f"{method:12s}: {g1.compare(g2, method=method):.6f}")

rng = np.random.default_rng(0) data = rng.standard_normal((3000, 2)) edges = compute_edges(data) g1 = DenseHypergrid(edges) g2 = DenseHypergrid(edges) g1.fit(data) g2.fit(data) for method in ["l1", "js", "kl"]: print(f"{method:12s}: {g1.compare(g2, method=method):.6f}")

l1          : 0.000000
js          : 0.000000
kl          : 0.000000

2. Shifted distribution — increasing divergence with shift magnitude¶

In [3]:

shifts = [0.0, 0.5, 1.0, 1.5, 2.0]
js_values = []

baseline = rng.standard_normal((2000, 2))
full_edges = compute_edges(np.vstack([baseline, baseline + max(shifts)]))

g_base = DenseHypergrid(full_edges)
g_base.fit(baseline)

for shift in shifts:
    shifted = baseline + shift
    g_shifted = DenseHypergrid(full_edges)
    g_shifted.fit(shifted)
    js_values.append(g_base.compare(g_shifted, method="js"))

plt.figure(figsize=(6, 3))
plt.plot(shifts, js_values, marker="o")
plt.xlabel("Distribution shift")
plt.ylabel("JS divergence")
plt.title("JS divergence vs distribution shift")
plt.tight_layout()
plt.show()

shifts = [0.0, 0.5, 1.0, 1.5, 2.0] js_values = [] baseline = rng.standard_normal((2000, 2)) full_edges = compute_edges(np.vstack([baseline, baseline + max(shifts)])) g_base = DenseHypergrid(full_edges) g_base.fit(baseline) for shift in shifts: shifted = baseline + shift g_shifted = DenseHypergrid(full_edges) g_shifted.fit(shifted) js_values.append(g_base.compare(g_shifted, method="js")) plt.figure(figsize=(6, 3)) plt.plot(shifts, js_values, marker="o") plt.xlabel("Distribution shift") plt.ylabel("JS divergence") plt.title("JS divergence vs distribution shift") plt.tight_layout() plt.show()

3. All divergence metrics side by side¶

In [4]:

g_shifted = DenseHypergrid(full_edges)
g_shifted.fit(baseline + 1.5)

methods = ["l1", "js", "kl"]
for m in methods:
    print(f"{m:12s}: {g_base.compare(g_shifted, method=m):.4f}")

g_shifted = DenseHypergrid(full_edges) g_shifted.fit(baseline + 1.5) methods = ["l1", "js", "kl"] for m in methods: print(f"{m:12s}: {g_base.compare(g_shifted, method=m):.4f}")

l1          : 1.4590
js          : 0.4045
kl          : 9.0464

4. Wasserstein distance (Earth Mover's Distance)¶

Uses LP — run on a small grid to keep it fast.

In [5]:

small_edges = [np.linspace(-3, 3, 7), np.linspace(-3, 3, 7)]

w1 = DenseHypergrid(small_edges)
w2 = DenseHypergrid(small_edges)
w1.fit(rng.standard_normal((500, 2)))
w2.fit(rng.standard_normal((500, 2)) + 1.5)

print(f"Wasserstein: {w1.compare(w2, method='wasserstein'):.4f}")

small_edges = [np.linspace(-3, 3, 7), np.linspace(-3, 3, 7)] w1 = DenseHypergrid(small_edges) w2 = DenseHypergrid(small_edges) w1.fit(rng.standard_normal((500, 2))) w2.fit(rng.standard_normal((500, 2)) + 1.5) print(f"Wasserstein: {w1.compare(w2, method='wasserstein'):.4f}")

Wasserstein: 1.9705

5. Marginal comparison¶

In [6]:

g_base.compare_marginal(g_shifted, dim=0)

g_base.compare_marginal(g_shifted, dim=0)

6. UMAP comparison¶

In [7]:

# Requires: pip install "hypergrid[umap]"
g_base.compare_umap(g_shifted)

# Requires: pip install "hypergrid[umap]" g_base.compare_umap(g_shifted)

c:\Users\cleme\PROJECTS\HYPERGRID\.venv\Lib\site-packages\tqdm\auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm