sklearn.covariance.ledoit_wolf(X, *, assume_centered=False, block_size=1000)[source]#

Estimate the shrunk Ledoit-Wolf covariance matrix.

Read more in the User Guide.

Xarray-like of shape (n_samples, n_features)

Data from which to compute the covariance estimate.

assume_centeredbool, default=False

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

block_sizeint, default=1000

Size of blocks into which the covariance matrix will be split. This is purely a memory optimization and does not affect results.

shrunk_covndarray of shape (n_features, n_features)

Shrunk covariance.


Coefficient in the convex combination used for the computation of the shrunk estimate.


The regularized (shrunk) covariance is:

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

where mu = trace(cov) / n_features


>>> import numpy as np
>>> from sklearn.covariance import empirical_covariance, ledoit_wolf
>>> real_cov = np.array([[.4, .2], [.2, .8]])
>>> rng = np.random.RandomState(0)
>>> X = rng.multivariate_normal(mean=[0, 0], cov=real_cov, size=50)
>>> covariance, shrinkage = ledoit_wolf(X)
>>> covariance
array([[0.44..., 0.16...],
       [0.16..., 0.80...]])
>>> shrinkage