sklearn.covariance
.GraphicalLasso¶
- class sklearn.covariance.GraphicalLasso(alpha=0.01, *, mode='cd', covariance=None, tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, eps=2.220446049250313e-16, 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.
- covariance“precomputed”, default=None
If covariance is “precomputed”, the input data in
fit
is assumed to be the covariance matrix. IfNone
, the empirical covariance is estimated from the dataX
.New in version 1.3.
- 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.
- epsfloat, default=eps
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Default is
np.finfo(np.float64).eps
.New in version 1.3.
- 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.
- costs_list of (objective, dual_gap) pairs
The list of values of the objective function and the dual gap at each iteration. Returned only if return_costs is True.
New in version 1.3.
- n_features_in_int
Number of features seen during fit.
New in version 0.24.
- feature_names_in_ndarray of shape (
n_features_in_
,) Names of features seen during fit. Defined only when
X
has feature names that are all strings.New in version 1.0.
See also
graphical_lasso
L1-penalized covariance estimator.
GraphicalLassoCV
Sparse inverse covariance with cross-validated choice of the l1 penalty.
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])Compute the Mean Squared Error between two covariance estimators.
fit
(X[, y])Fit the GraphicalLasso model to X.
Get metadata routing of this object.
get_params
([deep])Get parameters for this estimator.
Getter for the precision matrix.
mahalanobis
(X)Compute the squared Mahalanobis distances of given observations.
score
(X_test[, y])Compute the log-likelihood of
X_test
under the estimated Gaussian model.set_params
(**params)Set the parameters of this estimator.
set_score_request
(*[, X_test])Request metadata passed to the
score
method.- error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)[source]¶
Compute the Mean Squared Error between two covariance estimators.
- 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
self
andcomp_cov
covariance estimators.
- fit(X, y=None)[source]¶
Fit 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
Returns the instance itself.
- get_metadata_routing()[source]¶
Get metadata routing of this object.
Please check User Guide on how the routing mechanism works.
- Returns:
- routingMetadataRequest
A
MetadataRequest
encapsulating routing information.
- 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.
- 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.
- mahalanobis(X)[source]¶
Compute 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.
- score(X_test, y=None)[source]¶
Compute the log-likelihood of
X_test
under the estimated Gaussian model.The Gaussian model is defined by its mean and covariance matrix which are represented respectively by
self.location_
andself.covariance_
.- 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 andn_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 log-likelihood of
X_test
withself.location_
andself.covariance_
as estimators of the Gaussian model mean and covariance matrix respectively.
- 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.
- set_score_request(*, X_test: Union[bool, None, str] = '$UNCHANGED$') GraphicalLasso [source]¶
Request metadata passed to the
score
method.Note that this method is only relevant if
enable_metadata_routing=True
(seesklearn.set_config
). Please see User Guide on how the routing mechanism works.The options for each parameter are:
True
: metadata is requested, and passed toscore
if provided. The request is ignored if metadata is not provided.False
: metadata is not requested and the meta-estimator will not pass it toscore
.None
: metadata is not requested, and the meta-estimator will raise an error if the user provides it.str
: metadata should be passed to the meta-estimator with this given alias instead of the original name.
The default (
sklearn.utils.metadata_routing.UNCHANGED
) retains the existing request. This allows you to change the request for some parameters and not others.New in version 1.3.
Note
This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a
Pipeline
. Otherwise it has no effect.- Parameters:
- X_teststr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED
Metadata routing for
X_test
parameter inscore
.
- Returns:
- selfobject
The updated object.