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/ cross-validated choice of the l1 penalty

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, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy. Possible inputs for cv are: None, to use the default 3-fold cross-validation, integer, to specify the number of folds. An object to be used as a cross-validation generator. An iterable yielding train/test splits. For integer/None inputs `KFold` is used. Refer User Guide for the various cross-validation 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) : Log-likelihood score on left-out data across folds. n_iter_ : int Number of iterations run for the optimal alpha.

Notes

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.

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 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__(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:

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. :

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. :

fit(X, y=None) [source]

Fits the GraphLasso covariance model to X.

Parameters:

Parameters:	X : ndarray, shape (n_samples, n_features) Data from which to compute the covariance estimate

X : ndarray, shape (n_samples, n_features)

Data from which to compute the covariance estimate

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters:

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.

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:

Returns:	precision_ : array-like, The precision matrix associated to the current covariance object.

precision_ : array-like,

The precision matrix associated to the current covariance object.

mahalanobis(observations) [source]

Computes the squared Mahalanobis distances of given observations.

Parameters:

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.

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) [source]

Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.

Parameters:

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.

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) [source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it?s possible to update each component of a nested object.