scikits.learn.covariance.LedoitWolf

class scikits.learn.covariance.LedoitWolf(store_precision=True)

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 Reference)

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

__init__(store_precision=True)

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.

mse(comp_cov)

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 which to be compared to.

Returns :

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

`self` and `comp_cov` covariance estimators. :

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.