scikit-covtest: Covariance Matrix Hypothesis Testing Toolkit

scikit-covtest is a Python package designed for hypothesis testing on covariance matrices. It provides a comprehensive suite of statistical tests for high-dimensional data, including one-sample tests (Identity, Sphericity), two-sample tests (Equality), and multi-sample tests (Proportionality).

Features

• One-Sample Tests:
  • Identity: Test if the covariance matrix is the identity matrix ($\Sigma = I$).
  • Sphericity: Test if the covariance matrix is proportional to the identity matrix ($\Sigma = \lambda I$).
• Two-Sample Tests:
  • Equality: Test if two covariance matrices are equal ($\Sigma_1 = \Sigma_2$).
  • Proportionality: Test if multiple covariance matrices are proportional to each other ($\Sigma_i = c_i \Sigma$).
• High-Dimensional Support: Many tests are designed to work well even when the number of features ($p$) exceeds the number of samples ($n$).
• Scikit-Learn Compatible: Designed to integrate smoothly with the scientific Python ecosystem.

Installation

You can install scikit-covtest directly from the source:

git clone https://github.com/bystrogenomics/scikit-covtest.git
cd scikit-covtest
pip install .

Usage Examples

1. One-Sample Test: Identity

Test if the covariance matrix of a dataset is the Identity matrix.

import numpy as np
from covtest.methods.hypothesis_identity import fisher_single_sample

# Generate synthetic data (Identity covariance)
rng = np.random.default_rng(42)
X = rng.normal(size=(50, 10))  # n=50, p=10

# Perform Fisher's test for Identity
result = fisher_single_sample(X, Sigma="identity")
print(f"Statistic: {result['stat']:.4f}, P-value: {result['p_value']:.4f}")

2. Two-Sample Test: Equality

Test if two datasets share the same covariance matrix.

import numpy as np
from covtest.methods.hypothesis_two_sample import schott_2001

# Generate two datasets with the same covariance
rng = np.random.default_rng(42)
X1 = rng.normal(size=(30, 5))
X2 = rng.normal(size=(40, 5))

# Perform Schott's test for equality of covariance matrices
result = schott_2001(X1, X2)
print(f"Statistic: {result['stat']:.4f}, P-value: {result['p_value']:.4f}")

3. Multi-Sample Test: Proportionality

Test if covariance matrices from multiple groups are proportional.

import numpy as np
from covtest.methods.hypothesis_proportionality import bartlett_adjusted_proportionality_test

# Generate data for 2 groups with proportional covariances
rng = np.random.default_rng(42)
cov = np.eye(5)
X1 = rng.multivariate_normal(mean=np.zeros(5), cov=cov, size=30)
X2 = rng.multivariate_normal(mean=np.zeros(5), cov=2*cov, size=30) # Proportional by factor 2

# Perform Bartlett-adjusted test for proportionality
result = bartlett_adjusted_proportionality_test(X1, X2)
print(f"Statistic: {result['stat']:.4f}, P-value: {result['p_value']:.4f}")

Dependencies

• numpy
• scipy
• scikit-learn
• pandas
• tqdm
• matplotlib
• statsmodels
• cvxpy

License

This project is licensed under the MIT License. See the LICENSE file for details.