`sklearn.covariance`.EmpiricalCovariance¶

class sklearn.covariance.EmpiricalCovariance(*, store_precision=True, assume_centered=False)[source]¶

Maximum likelihood covariance estimator.

See also

EllipticEnvelope: An object for detecting outliers in a Gaussian distributed dataset.
GraphicalLasso: Sparse inverse covariance estimation with an l1-penalized estimator.
LedoitWolf: LedoitWolf Estimator.
MinCovDet: Minimum Covariance Determinant (robust estimator of covariance).
OAS: Oracle Approximating Shrinkage Estimator.
ShrunkCovariance: Covariance estimator with shrinkage.

Examples

>>> import numpy as np
>>> from sklearn.covariance import EmpiricalCovariance
>>> from sklearn.datasets import make_gaussian_quantiles
>>> real_cov = np.array([[.8, .3],
...                      [.3, .4]])
>>> rng = np.random.RandomState(0)
>>> X = rng.multivariate_normal(mean=[0, 0],
...                             cov=real_cov,
...                             size=500)
>>> cov = EmpiricalCovariance().fit(X)
>>> cov.covariance_
array([[0.7569..., 0.2818...],
       [0.2818..., 0.3928...]])
>>> cov.location_
array([0.0622..., 0.0193...])

Methods

`error_norm`(comp_cov[, norm, scaling, squared])	Compute the Mean Squared Error between two covariance estimators.
`fit`(X[, y])	Fit the maximum likelihood covariance estimator to X.
`get_params`([deep])	Get parameters for this estimator.
`get_precision`()	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.

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 maximum likelihood covariance estimator 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_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.

Examples using `sklearn.covariance.EmpiricalCovariance`¶

Robust covariance estimation and Mahalanobis distances relevance

Robust vs Empirical covariance estimate

Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood

sklearn.covariance.EmpiricalCovariance¶

Examples using sklearn.covariance.EmpiricalCovariance¶

`sklearn.covariance`.EmpiricalCovariance¶

Examples using `sklearn.covariance.EmpiricalCovariance`¶