shrunk_covariance#

sklearn.covariance.shrunk_covariance(emp_cov,shrinkage=0.1)[source]#

Calculate covariance matrices shrunk on the diagonal.

Read more in theUser Guide.

Parameters:

emp_covarray-like of shape (…, n_features, n_features)

Covariance matrices to be shrunk, at least 2D ndarray.

shrinkagefloat, default=0.1

Coefficient in the convex combination used for the computationof the shrunk estimate. Range is [0, 1].

Returns:

shrunk_covndarray of shape (…, n_features, n_features)

Shrunk covariance matrices.

Notes

The regularized (shrunk) covariance is given by:

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

wheremu=trace(cov)/n_features.

Examples

>>>importnumpyasnp>>>fromsklearn.datasetsimportmake_gaussian_quantiles>>>fromsklearn.covarianceimportempirical_covariance,shrunk_covariance>>>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)>>>shrunk_covariance(empirical_covariance(X))array([[0.739, 0.254],       [0.254, 0.411]])