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.
Changed in version v0.20: GraphLasso has been renamed to GraphicalLasso
- Parameters
- alphafloat, default=0.01
The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance. Range is (0, inf].
- 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.
- tolfloat, default=1e-4
The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped. Range is (0, inf].
- enet_tolfloat, default=1e-4
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’. Range is (0, inf].
- max_iterint, default=100
The maximum number of iterations.
- verbosebool, default=False
If verbose is True, the objective function and dual gap are plotted at each iteration.
- assume_centeredbool, 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_ndarray of shape (n_features,)
Estimated location, i.e. the estimated mean.
- covariance_ndarray of shape (n_features, n_features)
Estimated covariance matrix
- precision_ndarray of shape (n_features, n_features)
Estimated pseudo inverse matrix.
- n_iter_int
Number of iterations run.
See also
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(comp_cov[, norm, scaling, squared])Computes the Mean Squared Error between two covariance estimators.
fit(X[, y])Fits the GraphicalLasso model to X.
get_params([deep])Get parameters for this estimator.
Getter for the precision matrix.
mahalanobis(X)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.
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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_covarray-like of shape (n_features, n_features)
The covariance to compare with.
- norm{“frobenius”, “spectral”}, default=”frobenius”
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, default=True
If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
- squaredbool, default=True
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
- resultfloat
The Mean Squared Error (in the sense of the Frobenius norm) between
selfandcomp_covcovariance estimators.
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fit(X, y=None)[source]¶ Fits the GraphicalLasso model to X.
- Parameters
- Xarray-like of shape (n_samples, n_features)
Data from which to compute the covariance estimate
- yIgnored
Not used, present for API consistency by convention.
- Returns
- selfobject
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get_params(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
- paramsdict
Parameter names mapped to their values.
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get_precision()[source]¶ Getter for the precision matrix.
- Returns
- precision_array-like of shape (n_features, n_features)
The precision matrix associated to the current covariance object.
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mahalanobis(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
- distndarray of shape (n_samples,)
Squared Mahalanobis distances of the observations.
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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
- 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).
- yIgnored
Not used, present for API consistency by convention.
- Returns
- resfloat
The likelihood of the data set with
self.covariance_as an estimator of its covariance matrix.
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set_params(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline). 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
- selfestimator instance
Estimator instance.