shrunk_covariance#
- sklearn.covariance.shrunk_covariance(emp_cov, shrinkage=0.1)[source]#
Calculate covariance matrices shrunk on the diagonal.
Read more in the User 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 computation of 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)
where
mu = trace(cov) / n_features
.Examples
>>> import numpy as np >>> from sklearn.datasets import make_gaussian_quantiles >>> from sklearn.covariance import empirical_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([[0.73..., 0.25...], [0.25..., 0.41...]])