sklearn.covariance.EmpiricalCovariance¶

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

Maximum likelihood covariance estimator

Read more in the User Guide.

Parameters

store_precisionbool

Specifies if the estimated precision is stored.

assume_centeredbool

If True, data are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data are centered before computation.

Attributes

location_array-like, shape (n_features,)

Estimated location, i.e. the estimated mean.

covariance_2D ndarray, shape (n_features, n_features)

Estimated covariance matrix

precision_2D ndarray, shape (n_features, n_features)

Estimated pseudo-inverse matrix. (stored only if store_precision is True)

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(self, comp_cov[, norm, scaling, …])	Computes the Mean Squared Error between two covariance estimators.
fit(self, X[, y])	Fits the Maximum Likelihood Estimator covariance model according to the given training data and parameters.
get_params(self[, deep])	Get parameters for this estimator.
get_precision(self)	Getter for the precision matrix.
mahalanobis(self, X)	Computes the squared Mahalanobis distances of given observations.
score(self, X_test[, y])	Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.
set_params(self, \*\*params)	Set the parameters of this estimator.

__init__(self, store_precision=True, assume_centered=False)[source]¶

Initialize self. See help(type(self)) for accurate signature.

error_norm(self, 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, shape = [n_features, n_features]

The covariance to compare with.

normstr

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

If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.

squaredbool

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

The Mean Squared Error (in the sense of the Frobenius norm) between

self and comp_cov covariance estimators.

fit(self, X, y=None)[source]¶

Fits the Maximum Likelihood Estimator covariance model according to the given training data and parameters.

Parameters

Xarray-like, shape = [n_samples, n_features]

Training data, where n_samples is the number of samples and n_features is the number of features.

y

not used, present for API consistence purpose.

Returns

selfobject

get_params(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepboolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsmapping of string to any

Parameter names mapped to their values.

get_precision(self)[source]¶

Getter for the precision matrix.

Returns

precision_array-like

The precision matrix associated to the current covariance object.

mahalanobis(self, X)[source]¶

Computes the squared Mahalanobis distances of given observations.

Parameters

Xarray-like, 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

distarray, shape = [n_samples,]

Squared Mahalanobis distances of the observations.

score(self, 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, 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).

y

not used, present for API consistence purpose.

Returns

resfloat

The likelihood of the data set with self.covariance_ as an estimator of its covariance matrix.

set_params(self, **params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns

self