sklearn.covariance
.GraphLassoCV¶

class
sklearn.covariance.
GraphLassoCV
(alphas=4, n_refinements=4, cv=None, tol=0.0001, enet_tol=0.0001, max_iter=100, mode=’cd’, n_jobs=1, verbose=False, assume_centered=False)[source]¶ Sparse inverse covariance w/ crossvalidated choice of the l1 penalty
Read more in the User Guide.
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 times the grid is refined. Not used if explicit values of alphas are passed.
cv : int, crossvalidation generator or an iterable, optional
Determines the crossvalidation splitting strategy. Possible inputs for cv are:
 None, to use the default 3fold crossvalidation,
 integer, to specify the number of folds.
 An object to be used as a crossvalidation generator.
 An iterable yielding train/test splits.
For integer/None inputs
KFold
is used.Refer User Guide for the various crossvalidation strategies that can be used here.
tol : positive float, optional
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, 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.
Attributes
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)) Loglikelihood score on leftout data across folds. n_iter_ (int) Number of iterations run for the optimal alpha. See also
Notes
The search for the optimal penalization parameter (alpha) is done on an iteratively refined grid: first the crossvalidated 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 wellconditioned estimate. The corresponding values of alpha then come out as missing values, but the optimum may be close to these missing values.
Methods
error_norm
(comp_cov[, norm, scaling, squared])Computes the Mean Squared Error between two covariance estimators. fit
(X[, y])Fits the GraphLasso covariance model to X. 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 loglikelihood 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__
(alphas=4, n_refinements=4, cv=None, tol=0.0001, enet_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).
Parameters: comp_cov : arraylike, 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.

fit
(X, y=None)[source]¶ Fits the GraphLasso covariance model to X.
Parameters: X : ndarray, shape (n_samples, n_features)
Data from which to compute the covariance estimate
y : (ignored)

get_params
(deep=True)[source]¶ 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
()[source]¶ Getter for the precision matrix.
Returns: precision_ : arraylike,
The precision matrix associated to the current covariance object.

grid_scores
¶ DEPRECATED: Attribute grid_scores was deprecated in version 0.19 and will be removed in 0.21. Use
grid_scores_
instead

mahalanobis
(observations)[source]¶ Computes the squared Mahalanobis distances of given observations.
Parameters: observations : arraylike, 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)[source]¶ Computes the loglikelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.
Parameters: X_test : arraylike, 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.