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

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


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 times the grid is refined. Not used if explicit values of alphas are passed.

cv : cross-validation generator, optional

see sklearn.cross_validation module. If None is passed, defaults 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 :

Maximum number of iterations.

mode: {‘cd’, ‘lars’} :

The Lasso solver to use: coordinate descent or LARS. Use LARS for very sparse underlying graphs, where number of features is greater than number of samples. 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 duality gap are printed at each iteration.

assume_centered : Boolean

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.


covariance_ : numpy.ndarray, shape (n_features, n_features)

Estimated covariance matrix.

precision_ : numpy.ndarray, shape (n_features, n_features)

Estimated precision matrix (inverse covariance).

alpha_ : float

Penalization parameter selected.

cv_alphas_ : list of float

All penalization parameters explored.

`grid_scores`: 2D numpy.ndarray (n_alphas, n_folds) :

Log-likelihood score on left-out data across folds.

n_iter_ : int

Number of iterations run for the optimal alpha.


The search for the optimal penalization parameter (alpha) is done on an iteratively refined grid: first the cross-validated scores on a grid are computed, then a new refined grid is centered around the maximum, and so on.

One of the challenges which is faced here 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.


__init__(alphas=4, n_refinements=4, cv=None, tol=0.0001, max_iter=100, mode='cd', n_jobs=1, verbose=False, assume_centered=False)[source]
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).


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.


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 GraphLasso covariance model to X.


X : ndarray, shape (n_samples, n_features)

Data from which to compute the covariance estimate


Get parameters for this estimator.


deep: boolean, optional :

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


params : mapping of string to any

Parameter names mapped to their values.


Getter for the precision matrix.


precision_ : array-like,

The precision matrix associated to the current covariance object.


Computes the squared Mahalanobis distances of given observations.


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.


mahalanobis_distance : array, shape = [n_observations,]

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.


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.


res : float

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


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 :