sklearn.covariance.GraphLasso

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

Sparse inverse covariance estimation with an l1-penalized estimator.

Read more in the User Guide.

Parameters:

alpha : positive float, default 0.01

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

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.

tol : positive float, default 1e-4

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

enet_tol : positive float, optional

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’.

max_iter : integer, default 100

The maximum number of iterations.

verbose : boolean, default False

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

assume_centered : boolean, 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:

covariance_ : array-like, shape (n_features, n_features)

Estimated covariance matrix

precision_ : array-like, shape (n_features, n_features)

Estimated pseudo inverse matrix.

n_iter_ : int

Number of iterations run.

See also

graph_lasso, GraphLassoCV

Methods

error_norm(comp_cov[, norm, scaling, squared])	Computes the Mean Squared Error between two covariance estimators.
fit(X[, y])
get_params([deep])	Get parameters for this estimator.
get_precision()	Getter for the precision matrix.
mahalanobis(observations)	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.

__init__(alpha=0.01, mode='cd', tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, assume_centered=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. :

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep: boolean, optional :

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

Returns:

params : mapping of string to any

Parameter names mapped to their values.

get_precision()

Getter for the precision matrix.

Returns:

precision_ : array-like,

The precision matrix associated to the current covariance object.

mahalanobis(observations)

Computes the squared Mahalanobis distances of given observations.

Parameters:

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

mahalanobis_distance : array, shape = [n_observations,]

Squared Mahalanobis distances of the observations.

score(X_test, y=None)

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. X_test is assumed to be drawn from the same distribution than the data used in fit (including centering).

y : not used, present for API consistence purpose.

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 this 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 :