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])
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. :

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 :