# sklearn.covariance.GraphicalLasso¶

class sklearn.covariance.GraphicalLasso(alpha=0.01, *, mode='cd', tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, assume_centered=False)[source]

Sparse inverse covariance estimation with an l1-penalized estimator.

Read more in the User Guide.

Changed in version v0.20: GraphLasso has been renamed to GraphicalLasso

Parameters
alphafloat, default=0.01

The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance. Range is (0, inf].

mode{‘cd’, ‘lars’}, default=’cd’

The Lasso solver to use: coordinate descent or LARS. Use LARS for very sparse underlying graphs, where p > n. Elsewhere prefer cd which is more numerically stable.

tolfloat, default=1e-4

The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped. Range is (0, inf].

enet_tolfloat, default=1e-4

The tolerance for the elastic net solver used to calculate the descent direction. This parameter controls the accuracy of the search direction for a given column update, not of the overall parameter estimate. Only used for mode=’cd’. Range is (0, inf].

max_iterint, default=100

The maximum number of iterations.

verbosebool, default=False

If verbose is True, the objective function and dual gap are plotted at each iteration.

assume_centeredbool, default=False

If True, data are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False, data are centered before computation.

Attributes
location_ndarray of shape (n_features,)

Estimated location, i.e. the estimated mean.

covariance_ndarray of shape (n_features, n_features)

Estimated covariance matrix

precision_ndarray of shape (n_features, n_features)

Estimated pseudo inverse matrix.

n_iter_int

Number of iterations run.

Examples

>>> import numpy as np
>>> from sklearn.covariance import GraphicalLasso
>>> true_cov = np.array([[0.8, 0.0, 0.2, 0.0],
...                      [0.0, 0.4, 0.0, 0.0],
...                      [0.2, 0.0, 0.3, 0.1],
...                      [0.0, 0.0, 0.1, 0.7]])
>>> np.random.seed(0)
>>> X = np.random.multivariate_normal(mean=[0, 0, 0, 0],
...                                   cov=true_cov,
...                                   size=200)
>>> cov = GraphicalLasso().fit(X)
>>> np.around(cov.covariance_, decimals=3)
array([[0.816, 0.049, 0.218, 0.019],
[0.049, 0.364, 0.017, 0.034],
[0.218, 0.017, 0.322, 0.093],
[0.019, 0.034, 0.093, 0.69 ]])
>>> np.around(cov.location_, decimals=3)
array([0.073, 0.04 , 0.038, 0.143])


Methods

 error_norm(comp_cov[, norm, scaling, squared]) Computes the Mean Squared Error between two covariance estimators. fit(X[, y]) Fits the GraphicalLasso model to X. get_params([deep]) Get parameters for this estimator. Getter for the precision matrix. Computes the squared Mahalanobis distances of given observations. score(X_test[, y]) Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix. set_params(**params) Set the parameters of this estimator.
error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)[source]

Computes the Mean Squared Error between two covariance estimators. (In the sense of the Frobenius norm).

Parameters
comp_covarray-like of shape (n_features, n_features)

The covariance to compare with.

norm{“frobenius”, “spectral”}, default=”frobenius”

The type of norm used to compute the error. Available error types: - ‘frobenius’ (default): sqrt(tr(A^t.A)) - ‘spectral’: sqrt(max(eigenvalues(A^t.A)) where A is the error (comp_cov - self.covariance_).

scalingbool, default=True

If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.

squaredbool, default=True

Whether to compute the squared error norm or the error norm. If True (default), the squared error norm is returned. If False, the error norm is returned.

Returns
resultfloat

The Mean Squared Error (in the sense of the Frobenius norm) between self and comp_cov covariance estimators.

fit(X, y=None)[source]

Fits the GraphicalLasso model to X.

Parameters
Xarray-like of shape (n_samples, n_features)

Data from which to compute the covariance estimate

yIgnored

Not used, present for API consistency by convention.

Returns
selfobject
get_params(deep=True)[source]

Get parameters for this estimator.

Parameters
deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns
paramsdict

Parameter names mapped to their values.

get_precision()[source]

Getter for the precision matrix.

Returns
precision_array-like of shape (n_features, n_features)

The precision matrix associated to the current covariance object.

mahalanobis(X)[source]

Computes the squared Mahalanobis distances of given observations.

Parameters
Xarray-like of shape (n_samples, n_features)

The observations, the Mahalanobis distances of the which we compute. Observations are assumed to be drawn from the same distribution than the data used in fit.

Returns
distndarray of shape (n_samples,)

Squared Mahalanobis distances of the observations.

score(X_test, y=None)[source]

Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.

Parameters
X_testarray-like of shape (n_samples, n_features)

Test data of which we compute the likelihood, where n_samples is the number of samples and n_features is the number of features. X_test is assumed to be drawn from the same distribution than the data used in fit (including centering).

yIgnored

Not used, present for API consistency by convention.

Returns
resfloat

The likelihood of the data set with self.covariance_ as an estimator of its covariance matrix.

set_params(**params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters
**paramsdict

Estimator parameters.

Returns
selfestimator instance

Estimator instance.