sklearn.covariance
.GraphicalLassoCV¶
- class sklearn.covariance.GraphicalLassoCV(*, alphas=4, n_refinements=4, cv=None, tol=0.0001, enet_tol=0.0001, max_iter=100, mode='cd', n_jobs=None, verbose=False, eps=2.220446049250313e-16, assume_centered=False)[source]¶
Sparse inverse covariance w/ cross-validated choice of the l1 penalty.
See glossary entry for cross-validation estimator.
Read more in the User Guide.
Changed in version v0.20: GraphLassoCV has been renamed to GraphicalLassoCV
- Parameters:
- alphasint or array-like of shape (n_alphas,), dtype=float, default=4
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. Range is [1, inf) for an integer. Range is (0, inf] for an array-like of floats.
- n_refinementsint, default=4
The number of times the grid is refined. Not used if explicit values of alphas are passed. Range is [1, inf).
- cvint, cross-validation generator or iterable, default=None
Determines the cross-validation splitting strategy. Possible inputs for cv are:
None, to use the default 5-fold cross-validation,
integer, to specify the number of folds.
An iterable yielding (train, test) splits as arrays of indices.
For integer/None inputs
KFold
is used.Refer User Guide for the various cross-validation strategies that can be used here.
Changed in version 0.20:
cv
default value if None changed from 3-fold to 5-fold.- 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
Maximum number of iterations.
- mode{‘cd’, ‘lars’}, default=’cd’
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_jobsint, default=None
Number of jobs to run in parallel.
None
means 1 unless in ajoblib.parallel_backend
context.-1
means using all processors. See Glossary for more details.Changed in version v0.20:
n_jobs
default changed from 1 to None- verbosebool, default=False
If verbose is True, the objective function and duality gap are printed 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 precision matrix (inverse covariance).
- 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.
- alpha_float
Penalization parameter selected.
- cv_results_dict of ndarrays
A dict with keys:
- alphasndarray of shape (n_alphas,)
All penalization parameters explored.
- split(k)_test_scorendarray of shape (n_alphas,)
Log-likelihood score on left-out data across (k)th fold.
New in version 1.0.
- mean_test_scorendarray of shape (n_alphas,)
Mean of scores over the folds.
New in version 1.0.
- std_test_scorendarray of shape (n_alphas,)
Standard deviation of scores over the folds.
New in version 1.0.
- n_iter_int
Number of iterations run for the optimal alpha.
- 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.
GraphicalLasso
Sparse inverse covariance estimation with an l1-penalized estimator.
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.In
fit
, once the best parameteralpha
is found through cross-validation, the model is fit again using the entire training set.Examples
>>> import numpy as np >>> from sklearn.covariance import GraphicalLassoCV >>> 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 = GraphicalLassoCV().fit(X) >>> np.around(cov.covariance_, decimals=3) array([[0.816, 0.051, 0.22 , 0.017], [0.051, 0.364, 0.018, 0.036], [0.22 , 0.018, 0.322, 0.094], [0.017, 0.036, 0.094, 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 covariance 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 covariance 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] = '$UNCHANGED$') GraphicalLassoCV [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.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.
Examples using sklearn.covariance.GraphicalLassoCV
¶
Sparse inverse covariance estimation
Visualizing the stock market structure