separability.comparator.py

class rings.separability.comparator.KSComparator

Comparator that uses the Kolmogorov-Smirnov test to compare two distributions.

This class implements a statistical test based on the Kolmogorov-Smirnov (KS) statistic to determine if two samples come from the same distribution. It uses permutation testing to empirically determine significance, making it suitable for small sample sizes where asymptotic approximations may not be reliable.

__call__(x, y, n_permutations=10_000, alpha=0.01, n_hypotheses=1, random_state=42, \*\*kwargs)

Compare two samples using Kolmogorov-Smirnov test with permutation testing.

Examples

>>> import numpy as np
>>> from rings.separability.comparator import KSComparator
>>>
>>> # Create two samples from different distributions
>>> x = np.random.normal(0, 1, 20)  # Standard normal
>>> y = np.random.normal(1, 1, 20)  # Shifted normal
>>>
>>> # Compare distributions with KS test
>>> comparator = KSComparator()
>>> result = comparator(x, y, n_permutations=1000, alpha=0.05)
>>>
>>> # Interpret results
>>> print(f"KS statistic: {result['score']}")
>>> print(f"p-value: {result['pvalue']}")
>>> print(f"Significant: {result['significant']}")

Notes

The Kolmogorov-Smirnov test measures the maximum difference between the empirical cumulative distribution functions of two samples. It is sensitive to differences in both location and shape of distributions.

class rings.separability.comparator.WilcoxonComparator

Comparator that uses the Wilcoxon signed-rank test to compare two distributions.

This class implements a statistical test based on the Wilcoxon signed-rank test for paired samples. It uses permutation testing to empirically determine significance, making it suitable for small sample sizes or when assumptions for parametric tests are not met.

__call__(x, y, n_permutations=10_000, alpha=0.01, n_hypotheses=1, random_state=42, \*\*kwargs)

Compare two samples using Wilcoxon signed-rank test with permutation testing.

Examples

>>> import numpy as np
>>> from rings.separability.comparator import WilcoxonComparator
>>>
>>> # Create paired samples (must be equal length)
>>> np.random.seed(42)
>>> x = np.random.normal(0, 1, 20)
>>> y = x + np.random.normal(0.5, 0.5, 20)  # Same as x with shift + noise
>>>
>>> # Compare distributions
>>> comparator = WilcoxonComparator()
>>> result = comparator(x, y, n_permutations=1000, alpha=0.05)
>>>
>>> # Interpret results
>>> print(f"Wilcoxon statistic: {result['score']}")
>>> print(f"p-value: {result['pvalue']}")
>>> print(f"Significant: {result['significant']}")

Notes

The Wilcoxon signed-rank test compares paired samples by ranking the absolute differences between pairs and summing the ranks of positive differences. Unlike the t-test, it does not require the differences to be normally distributed.

This implementation requires paired samples of equal length.