space-graph

space-graph estimates sparse partial-correlation networks from tabular data.

Given a data matrix, it finds pairs of variables that remain related after accounting for all other variables. This is useful for network discovery in high-dimensional settings such as genomics, where the number of variables may be large relative to the number of samples.

The package implements SPACE (Sparse Partial Correlation Estimation) from Peng et al. (2009): Sparse Partial Correlation Estimation for High-Dimensional Data.

Install

pip install space-graph

Quick Start

import numpy as np
from space_graph import SPACE

X = np.random.randn(100, 20)

model = SPACE(alpha=0.5).fit(X)

partial_correlations = model.partial_correlation_

partial_correlations is a square matrix. Entry (i, j) is the estimated partial correlation between variables i and j. Values close to zero indicate no direct relationship after conditioning on the other variables.

Choosing alpha

alpha controls sparsity:

• larger alpha -> fewer edges
• smaller alpha -> more edges

You can choose alpha from a grid using BIC or AIC:

alphas = np.geomspace(0.01, 1.0, 20)

template = SPACE(max_outer_iter=3)
best_alpha = template.select_alpha(X, alphas, criterion='bic')

model = SPACE(alpha=best_alpha, max_outer_iter=3).fit(X)

BIC is the default and is usually more conservative. AIC often selects a denser network:

best_alpha = template.select_alpha(X, alphas, criterion='aic')

To inspect the scores:

best_alpha, scores = template.select_alpha(
    X,
    alphas,
    criterion='bic',
    return_curve=True,
)

Important Options

SPACE(
    alpha=0.5,
    gamma=1.0,
    weight='uniform',
    standardize=True,
    backend='auto',
)

• alpha: regularization strength. Higher values produce sparser networks.
• gamma: mix between L1 sparsity and L2 shrinkage. The default 1.0 is pure L1.
• weight: node weighting scheme. Use 'uniform' for most cases.
• standardize: centers and scales columns before fitting.
• backend: 'auto' uses the Rust backend when available and falls back to NumPy.

Output

After fitting:

model.partial_correlation_
model.sig_
model.weight_

The main result is partial_correlation_, a symmetric matrix with unit diagonal.

Citation

If you use this package, please cite:

Peng, J., Wang, P., Zhou, N., & Zhu, J. (2009). Sparse partial correlation estimation by joint sparse regression models. Journal of the American Statistical Association, 104(486), 735-746.

License

GPL-3.0-or-later.