sklearn.covariance
.LedoitWolf¶

class
sklearn.covariance.
LedoitWolf
(store_precision=True, assume_centered=False, block_size=1000)¶ LedoitWolf Estimator
LedoitWolf is a particular form of shrinkage, where the shrinkage coefficient is computed using O. Ledoit and M. Wolf’s formula as described in “A WellConditioned Estimator for LargeDimensional Covariance Matrices”, Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365411.
Read more in the User Guide.
Parameters: store_precision : bool, default=True
Specify if the estimated precision is stored.
assume_centered : bool, 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.
block_size : int, default=1000
Size of the blocks into which the covariance matrix will be split during its LedoitWolf estimation. This is purely a memory optimization and does not affect results.
Attributes
location_ (arraylike, shape (n_features,)) Estimated location, i.e. the estimated mean. covariance_ (arraylike, shape (n_features, n_features)) Estimated covariance matrix precision_ (arraylike, shape (n_features, n_features)) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage_ (float, 0 <= shrinkage <= 1) Coefficient in the convex combination used for the computation of the shrunk estimate. 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 WellConditioned Estimator for LargeDimensional Covariance Matrices”, Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365411.
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_ # doctest: +ELLIPSIS array([[0.4406..., 0.1616...], [0.1616..., 0.8022...]]) >>> cov.location_ array([ 0.0595... , 0.0075...])
Methods
error_norm
(comp_cov[, norm, scaling, squared])Computes the Mean Squared Error between two covariance estimators. fit
(X[, y])Fits the LedoitWolf shrunk covariance model according to the given training data and parameters. get_params
([deep])Get parameters for this estimator. get_precision
()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. 
__init__
(store_precision=True, assume_centered=False, block_size=1000)¶ Initialize self. See help(type(self)) for accurate signature.

error_norm
(comp_cov, norm='frobenius', scaling=True, squared=True)¶ Computes the Mean Squared Error between two covariance estimators. (In the sense of the Frobenius norm).
Parameters: comp_cov : arraylike, shape = [n_features, n_features]
The covariance to compare with.
norm : str
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_)
.scaling : bool
If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
squared : bool
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
(X, y=None)¶ Fits the LedoitWolf shrunk covariance model according to the given training data and parameters.
Parameters: X : arraylike, 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: self : object

get_params
(deep=True)¶ Get parameters for this estimator.
Parameters: deep : boolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns: params : mapping of string to any
Parameter names mapped to their values.

get_precision
()¶ Getter for the precision matrix.
Returns: precision_ : arraylike
The precision matrix associated to the current covariance object.

mahalanobis
(X)¶ Computes the squared Mahalanobis distances of given observations.
Parameters: X : arraylike, 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: dist : array, shape = [n_samples,]
Squared Mahalanobis distances of the observations.

score
(X_test, y=None)¶ Computes the loglikelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.
Parameters: X_test : arraylike, 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: res : float
The likelihood of the data set with self.covariance_ as an estimator of its covariance matrix.

set_params
(**params)¶ 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
