8.2.6. sklearn.covariance.GraphLassoCV

class sklearn.covariance.GraphLassoCV(alphas=4, n_refinements=4, cv=None, tol=0.0001, max_iter=100, mode='cd', n_jobs=1, verbose=False)

Sparse inverse covariance w/ cross-validated choice of the l1 penality

Parameters :

alphas: integer, or list positive float, optional :

If an integer is given, it fixes the number of points on the grids of alpha to be used. If a list is given, it gives the grid to be used. See the notes in the class docstring for more details.

n_refinements: strictly positive integer :

The number of time the grid is refined. Not used if explicit values of alphas are passed.

cv : crossvalidation generator, optional

see sklearn.cross_validation module. If None is passed, default to a 3-fold strategy

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

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.

n_jobs: int, optional :

number of jobs to run in parallel (default 1)

verbose: boolean, optional :

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

See also

graph_lasso, GraphLasso

Notes

The search for the optimal alpha is done on an iteratively refined grid: first the cross-validated scores on a grid are computed, then a new refined grid is center around the maximum...

One of the challenges that we have to face is that the solvers can fail to converge to a well-conditioned estimate. The corresponding values of alpha then come out as missing values, but the optimum may be close to these missing values.

Attributes

covariance_	array-like, shape (n_features, n_features)	Estimated covariance matrix
precision_	array-like, shape (n_features, n_features)	Estimated precision matrix (inverse covariance).
alpha_: float		Penalization parameter selected
cv_alphas_: list of float		All the penalization parameters explored
cv_scores: 2D array (n_alphas, n_folds)		The log-likelihood score on left-out data across the folds.

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 the estimator
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__(alphas=4, n_refinements=4, cv=None, tol=0.0001, max_iter=100, mode='cd', n_jobs=1, 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. :

get_params(deep=True)

Get parameters for the estimator

Parameters :

deep: boolean, optional :

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