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, default=True
Specifies if the estimated precision is stored.
 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 (default), 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 pseudoinverse 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
(comp_cov[, norm, scaling, squared])Computes the Mean Squared Error between two covariance estimators.
fit
(X[, y])Fits the Maximum Likelihood Estimator covariance model according to the given training data and parameters.
get_params
([deep])Get parameters for this estimator.
Getter for the precision matrix.
mahalanobis
(X)Computes the squared Mahalanobis distances of given observations.
score
(X_test[, y])Computes the loglikelihood of a Gaussian data set with
self.covariance_
as an estimator of its covariance matrix.set_params
(**params)Set the parameters of this estimator.

error_norm
(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_covarraylike 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]¶ Fits the Maximum Likelihood Estimator covariance model according to the given training data and parameters.
 Parameters
 Xarraylike 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 consistence purpose.
 Returns
 selfobject

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
 paramsmapping of string to any
Parameter names mapped to their values.

get_precision
()[source]¶ Getter for the precision matrix.
 Returns
 precision_arraylike of shape (n_features, n_features)
The precision matrix associated to the current covariance object.

mahalanobis
(X)[source]¶ Computes the squared Mahalanobis distances of given observations.
 Parameters
 Xarraylike 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]¶ Computes the loglikelihood of a Gaussian data set with
self.covariance_
as an estimator of its covariance matrix. Parameters
 X_testarraylike 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 consistence purpose.
 Returns
 resfloat
The likelihood of the data set with
self.covariance_
as an estimator of its covariance matrix.

set_params
(**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. Parameters
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.