`sklearn.covariance`.OAS¶

class sklearn.covariance.OAS(*, store_precision=True, assume_centered=False)[source]¶

Oracle Approximating Shrinkage Estimator.

See also

EllipticEnvelope: An object for detecting outliers in a Gaussian distributed dataset.
EmpiricalCovariance: Maximum likelihood covariance estimator.
GraphicalLasso: Sparse inverse covariance estimation with an l1-penalized estimator.
GraphicalLassoCV: Sparse inverse covariance with cross-validated choice of the l1 penalty.
LedoitWolf: LedoitWolf Estimator.
MinCovDet: Minimum Covariance Determinant (robust estimator of covariance).
ShrunkCovariance: Covariance estimator with shrinkage.

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 References)

References

“Shrinkage Algorithms for MMSE Covariance Estimation” Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010.

Examples

>>> import numpy as np
>>> from sklearn.covariance import OAS
>>> from sklearn.datasets import make_gaussian_quantiles
>>> 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)
>>> oas = OAS().fit(X)
>>> oas.covariance_
array([[0.7533..., 0.2763...],
       [0.2763..., 0.3964...]])
>>> oas.precision_
array([[ 1.7833..., -1.2431... ],
       [-1.2431...,  3.3889...]])
>>> oas.shrinkage_
0.0195...

Methods

`error_norm`(comp_cov[, norm, scaling, squared])	Compute the Mean Squared Error between two covariance estimators.
`fit`(X[, y])	Fit the Oracle Approximating Shrinkage covariance model to X.
`get_params`([deep])	Get parameters for this estimator.
`get_precision`()	Getter for the precision matrix.
`mahalanobis`(X)	Compute the squared Mahalanobis distances of given observations.
`score`(X_test[, y])	Compute the log-likelihood of `X_test` under the estimated Gaussian model.
`set_params`(**params)	Set the parameters of this estimator.

error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)[source]¶

Compute the Mean Squared Error between two covariance estimators.

Parameters:

comp_covarray-like of shape (n_features, n_features): The covariance to compare with.
norm{“frobenius”, “spectral”}, default=”frobenius”: The type of norm used to compute the error. Available error types: - ‘frobenius’ (default): sqrt(tr(A^t.A)) - ‘spectral’: sqrt(max(eigenvalues(A^t.A)) where A is the error (comp_cov - self.covariance_).
scalingbool, default=True: If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
squaredbool, default=True: Whether to compute the squared error norm or the error norm. If True (default), the squared error norm is returned. If False, the error norm is returned.

Returns:

resultfloat: The Mean Squared Error (in the sense of the Frobenius norm) between self and comp_cov covariance estimators.

fit(X, y=None)[source]¶

Fit the Oracle Approximating Shrinkage covariance model to X.

Parameters:

Xarray-like of shape (n_samples, n_features): Training data, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: Returns the instance itself.

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

get_precision()[source]¶

Getter for the precision matrix.

Returns:

precision_array-like of shape (n_features, n_features): The precision matrix associated to the current covariance object.

mahalanobis(X)[source]¶

Compute the squared Mahalanobis distances of given observations.

Parameters:

Xarray-like of shape (n_samples, n_features): The observations, the Mahalanobis distances of the which we compute. Observations are assumed to be drawn from the same distribution than the data used in fit.

Returns:

distndarray of shape (n_samples,): Squared Mahalanobis distances of the observations.

score(X_test, y=None)[source]¶

Compute the log-likelihood of X_test under the estimated Gaussian model.

The Gaussian model is defined by its mean and covariance matrix which are represented respectively by self.location_ and self.covariance_.

Parameters:

X_testarray-like of 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. X_test is assumed to be drawn from the same distribution than the data used in fit (including centering).
yIgnored: Not used, present for API consistency by convention.

Returns:

resfloat: The log-likelihood of X_test with self.location_ and self.covariance_ as estimators of the Gaussian model mean and covariance matrix respectively.

set_params(**params)[source]¶

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

Examples using `sklearn.covariance.OAS`¶

Normal, Ledoit-Wolf and OAS Linear Discriminant Analysis for classification

Ledoit-Wolf vs OAS estimation

Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood

sklearn.covariance.OAS¶

Examples using sklearn.covariance.OAS¶

`sklearn.covariance`.OAS¶

Examples using `sklearn.covariance.OAS`¶