8.2.3. sklearn.covariance.LedoitWolf

class sklearn.covariance.LedoitWolf(store_precision=True, assume_centered=False)

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.

Parameters :

store_precision : bool

Specify if the estimated precision is stored

Notes

The regularised covariance is:

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

where mu = trace(cov) / n_features and shinkage 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.

Attributes

covariance_	array-like, shape (n_features, n_features)	Estimated covariance matrix
precision_	array-like, 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.

Methods

error_norm(comp_cov[, norm, scaling, squared])	Computes the Mean Squared Error between two covariance estimators.
fit(X[, assume_centered])	Fits the Ledoit-Wolf shrunk covariance model
mahalanobis(observations)	Computes the mahalanobis distances of given observations.
score(X_test[, assume_centered])	Computes the log-likelihood of a gaussian data set with self.covariance_ as an estimator of its covariance matrix.
set_params(**params)	Set the parameters of the estimator.

__init__(store_precision=True, assume_centered=False)

Parameters :

store_precision: bool :

Specify if the estimated precision is stored

assume_centered: Boolean :

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

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: array-like, 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, assume_centered=False)

Fits the Ledoit-Wolf shrunk covariance model according to the given training data and parameters.

Parameters :

X : array-like, shape = [n_samples, n_features]

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

assume_centered: Boolean :

If True, data are not centered before computation. Usefull to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data are centered before computation.

Returns :

self : object

Returns self.

mahalanobis(observations)

Computes the mahalanobis distances of given observations.

The provided observations are assumed to be centered. One may want to center them using a location estimate first.

Parameters :

observations: array-like, shape = [n_observations, n_features] :

The observations, the Mahalanobis distances of the which we compute.

Returns :

mahalanobis_distance: array, shape = [n_observations,] :

Mahalanobis distances of the observations.

score(X_test, assume_centered=False)

Computes the log-likelihood of a gaussian data set with self.covariance_ as an estimator of its covariance matrix.

Parameters :

X_test : array-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.

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 the estimator.

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

Returns :self :