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, assume_centered=False)

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 : 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.

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.

See also

graph_lasso, GraphLasso

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, max_iter=100, mode='cd', n_jobs=1, verbose=False, assume_centered=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. :

fit(X, y=None)

Fits the GraphLasso covariance model to X.

Parameters:

X : ndarray, shape (n_samples, n_features)

Data from which to compute the covariance estimate

get_params(deep=True)

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()

Getter for the precision matrix.

Returns:

precision_ : array-like,

The precision matrix associated to the current covariance object.

mahalanobis(observations)

Computes the squared Mahalanobis distances of given observations.

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.

score(X_test, y=None)

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. 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)

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 :

Examples using sklearn.covariance.GraphLassoCV

Visualizing the stock market structure

Sparse inverse covariance estimation