sklearn.covariance.GraphicalLasso¶

class sklearn.covariance.GraphicalLasso(alpha=0.01, mode='cd', tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, assume_centered=False)[source]¶

Sparse inverse covariance estimation with an l1-penalized estimator.

Read more in the User Guide.

Parameters

alphapositive float, default 0.01

The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance.

mode{‘cd’, ‘lars’}, default ‘cd’

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.

tolpositive float, default 1e-4

The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped.

enet_tolpositive 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_iterinteger, default 100

The maximum number of iterations.

verboseboolean, default False

If verbose is True, the objective function and dual gap are plotted at each iteration.

assume_centeredboolean, default False

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

location_array-like, shape (n_features,)

Estimated location, i.e. the estimated mean.

covariance_array-like, shape (n_features, n_features)

Estimated covariance matrix

precision_array-like, shape (n_features, n_features)

Estimated pseudo inverse matrix.

n_iter_int

Number of iterations run.

See also

graphical_lasso, GraphicalLassoCV

Examples

>>> import numpy as np
>>> from sklearn.covariance import GraphicalLasso
>>> true_cov = np.array([[0.8, 0.0, 0.2, 0.0],
...                      [0.0, 0.4, 0.0, 0.0],
...                      [0.2, 0.0, 0.3, 0.1],
...                      [0.0, 0.0, 0.1, 0.7]])
>>> np.random.seed(0)
>>> X = np.random.multivariate_normal(mean=[0, 0, 0, 0],
...                                   cov=true_cov,
...                                   size=200)
>>> cov = GraphicalLasso().fit(X)
>>> np.around(cov.covariance_, decimals=3)
array([[0.816, 0.049, 0.218, 0.019],
       [0.049, 0.364, 0.017, 0.034],
       [0.218, 0.017, 0.322, 0.093],
       [0.019, 0.034, 0.093, 0.69 ]])
>>> np.around(cov.location_, decimals=3)
array([0.073, 0.04 , 0.038, 0.143])

Methods

error_norm(self, comp_cov[, norm, scaling, …])	Computes the Mean Squared Error between two covariance estimators.
fit(self, X[, y])	Fits the GraphicalLasso model to X.
get_params(self[, deep])	Get parameters for this estimator.
get_precision(self)	Getter for the precision matrix.
mahalanobis(self, X)	Computes the squared Mahalanobis distances of given observations.
score(self, X_test[, y])	Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.
set_params(self, \*\*params)	Set the parameters of this estimator.

__init__(self, alpha=0.01, mode='cd', tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, assume_centered=False)[source]¶

Initialize self. See help(type(self)) for accurate signature.

error_norm(self, 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_covarray-like of shape (n_features, n_features)

The covariance to compare with.

normstr

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_).

scalingbool

If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.

squaredbool

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(self, X, y=None)[source]¶

Fits the GraphicalLasso model to X.

Parameters

Xndarray, shape (n_samples, n_features)

Data from which to compute the covariance estimate

y(ignored)

get_params(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepbool, default=True

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

Returns

paramsmapping of string to any

Parameter names mapped to their values.

get_precision(self)[source]¶

Getter for the precision matrix.

Returns

precision_array-like

The precision matrix associated to the current covariance object.

mahalanobis(self, X)[source]¶

Computes the squared Mahalanobis distances of given observations.

Parameters

Xarray-like of shape (n_samples, 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

distarray, shape = [n_samples,]

Squared Mahalanobis distances of the observations.

score(self, 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

X_testarray-like of 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

resfloat

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

set_params(self, **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.

Parameters

**paramsdict

Estimator parameters.

Returns

selfobject

Estimator instance.