Implementation:Scikit learn Scikit learn GraphicalLasso

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Machine Learning, Covariance Estimation
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for sparse inverse covariance estimation with L1 penalty provided by scikit-learn.

Description

This module implements the GraphicalLasso and GraphicalLassoCV estimators for sparse inverse covariance (precision) matrix estimation using an L1 penalty. The L1 penalty encourages sparsity in the precision matrix, revealing conditional independence structure between features. GraphicalLassoCV adds cross-validated selection of the regularization parameter alpha. The module uses coordinate descent and LARS solvers internally for optimization.

Usage

Use GraphicalLasso to estimate sparse precision matrices when you want to discover the conditional independence structure in your data, such as in gene regulatory network inference or financial risk modeling.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/covariance/_graph_lasso.py

Signature

class GraphicalLasso(BaseGraphicalLasso):
    """Sparse inverse covariance estimation with an l1-penalized estimator."""

    def __init__(
        self,
        alpha=0.01,
        *,
        mode="cd",
        tol=1e-4,
        enet_tol=1e-4,
        max_iter=100,
        verbose=False,
        assume_centered=False,
    ):
        ...

class GraphicalLassoCV(BaseGraphicalLasso):
    """Sparse inverse covariance w/ cross-validated choice of the l1 penalty."""

    def __init__(
        self,
        *,
        alphas=4,
        n_refinements=4,
        cv=None,
        tol=1e-4,
        enet_tol=1e-4,
        max_iter=100,
        mode="cd",
        n_jobs=None,
        verbose=False,
        assume_centered=False,
    ):
        ...

Import

from sklearn.covariance import GraphicalLasso, GraphicalLassoCV

I/O Contract

Inputs

Name	Type	Required	Description
X	array-like of shape (n_samples, n_features)	Yes	Training data for covariance estimation
alpha	float	No	Regularization parameter for L1 penalty (default: 0.01)
mode	str	No	Solver: 'cd' for coordinate descent or 'lars' (default: 'cd')
tol	float	No	Convergence tolerance (default: 1e-4)
max_iter	int	No	Maximum number of iterations (default: 100)
assume_centered	bool	No	Whether data is centered (default: False)

Outputs

Name	Type	Description
covariance_	ndarray of shape (n_features, n_features)	Estimated covariance matrix
precision_	ndarray of shape (n_features, n_features)	Estimated sparse precision matrix
alpha_	float	Selected alpha value (GraphicalLassoCV only)
n_iter_	int	Number of iterations run

Usage Examples

Basic Usage

import numpy as np
from sklearn.covariance import GraphicalLassoCV

# Generate sample data with known structure
rng = np.random.RandomState(42)
n_samples, n_features = 100, 20
X = rng.randn(n_samples, n_features)

# Fit GraphicalLasso with cross-validated alpha
model = GraphicalLassoCV(cv=5).fit(X)
print("Selected alpha:", model.alpha_)
print("Precision matrix sparsity:", (model.precision_ == 0).mean())

Related Pages

• Principle:Scikit_learn_Scikit_learn_Covariance_Estimation