Toggle Menu
Prev Up Next

scikit-learn 1.3.2
Other versions

Please cite us if you use the software.

# `sklearn.covariance`.oas

sklearn.covariance.oas(X, *, assume_centered=False)

  Estimate covariance with the Oracle Approximating Shrinkage as proposed in [1].

  Read more in the User Guide.

  Parameters:
    X array-like of shape (n_samples, n_features)

      Data from which to compute the covariance estimate.

    assume_centered bool, 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.

  Returns:
    shrunk_cov array-like of shape (n_features, n_features)

      Shrunk covariance.

    shrinkage float

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

  Notes

  The regularised covariance is:

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

  where mu = trace(cov) / n_features and shrinkage is given by the OAS formula (see [1]).

  The shrinkage formulation implemented here differs from Eq. 23 in [1]. In the original article, formula (23) states that 2/p (p being the number of features) is multiplied by Trace(cov*cov) in both the numerator and denominator, but this operation is omitted because for a large p, the value of 2/p is so small that it doesn’t affect the value of the estimator.

  References

  [1] (1,2,3)

  “Shrinkage algorithms for MMSE covariance estimation.”, Chen, Y., Wiesel, A., Eldar, Y. C., & Hero, A. O. IEEE Transactions on Signal Processing, 58(10), 5016-5029, 2010.