8.2.5. sklearn.covariance.GraphLasso

class sklearn.covariance.GraphLasso(alpha=0.01, mode='cd', tol=0.0001, max_iter=100, verbose=False)

Sparse inverse covariance estimation with an l1-penalized estimator.

Parameters :

alpha: positive float, optional :

The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance

cov_init: 2D array (n_features, n_features), optional :

The initial guess for the covariance

mode: {‘cd’, ‘lars’} :

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.

tol: positive float, optional :

The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped

max_iter: integer, optional :

The maximum number of iterations

verbose: boolean, optional :

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

See also

graph_lasso, GraphLassoCV

Attributes

covariance_	array-like, shape (n_features, n_features)	Estimated covariance matrix
precision_	array-like, shape (n_features, n_features)	Estimated pseudo inverse matrix.

Methods

error_norm(comp_cov[, norm, scaling, squared])	Computes the Mean Squared Error between two covariance estimators.
fit(X[, y])
mahalanobis(observations)	Computes the mahalanobis distances of given observations.
score(X_test[, assume_centered])	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 the estimator.

__init__(alpha=0.01, mode='cd', tol=0.0001, max_iter=100, verbose=False)

error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)

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

Parameters :

comp_cov: array-like, shape = [n_features, n_features] :

The covariance to compare with.

norm: str :

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_).

scaling: bool :

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

squared: bool :

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 :

The Mean Squared Error (in the sense of the Frobenius norm) between :

`self` and `comp_cov` covariance estimators. :

mahalanobis(observations)

Computes the mahalanobis distances of given observations.

The provided observations are assumed to be centered. One may want to center them using a location estimate first.

Parameters :

observations: array-like, shape = [n_observations, n_features] :

The observations, the Mahalanobis distances of the which we compute.

Returns :

mahalanobis_distance: array, shape = [n_observations,] :

Mahalanobis distances of the observations.

score(X_test, assume_centered=False)

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

Parameters :

X_test : array-like, 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.

Returns :

res : float

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

set_params(**params)

Set the parameters of the estimator.

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

Returns :self :