LedoitWolf#

class sklearn.covariance.LedoitWolf(*, store_precision=True, assume_centered=False, block_size=1000)[source]#

LedoitWolf Estimator.

Ledoit-Wolf is a particular form of shrinkage, where the shrinkage coefficient is computed using O. Ledoit and M. Wolf’s formula as described in “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices”, Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411.

See also

EllipticEnvelope: An object for detecting outliers in a Gaussian distributed dataset.
EmpiricalCovariance: Maximum likelihood covariance estimator.
GraphicalLasso: Sparse inverse covariance estimation with an l1-penalized estimator.
GraphicalLassoCV: Sparse inverse covariance with cross-validated choice of the l1 penalty.
MinCovDet: Minimum Covariance Determinant (robust estimator of covariance).
OAS: Oracle Approximating Shrinkage Estimator.
ShrunkCovariance: Covariance estimator with shrinkage.

Notes

The regularised covariance is:

(1 - shrinkage) * cov + shrinkage * mu * np.identity(n_features)

where mu = trace(cov) / n_features and shrinkage is given by the Ledoit and Wolf formula (see References)

References

“A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices”, Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411.

Examples

>>> import numpy as np
>>> from sklearn.covariance import LedoitWolf
>>> real_cov = np.array([[.4, .2],
...                      [.2, .8]])
>>> np.random.seed(0)
>>> X = np.random.multivariate_normal(mean=[0, 0],
...                                   cov=real_cov,
...                                   size=50)
>>> cov = LedoitWolf().fit(X)
>>> cov.covariance_
array([[0.4406..., 0.1616...],
       [0.1616..., 0.8022...]])
>>> cov.location_
array([ 0.0595... , -0.0075...])

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 and comp_cov covariance estimators.

fit(X, y=None)[source]#

Fit the Ledoit-Wolf shrunk covariance model to X.

Parameters:

Xarray-like of shape (n_samples, n_features): Training data, where n_samples is the number of samples and n_features is the number of features.
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_ and self.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 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 log-likelihood of X_test with self.location_ and self.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.

Gallery examples#

Ledoit-Wolf vs OAS estimation

Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood

Model selection with Probabilistic PCA and Factor Analysis (FA)