Oracle Approximating Shrinkage Estimator.
Read more in the User Guide.
Specify if the estimated precision is stored.
If True, data will not be centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data will be centered before computation.
Estimated covariance matrix.
Estimated location, i.e. the estimated mean.
Estimated pseudo inverse matrix. (stored only if store_precision is True)
coefficient in the convex combination used for the computation of the shrunk estimate. Range is [0, 1].
Number of features seen during fit.
Added in version 0.24.
n_features_in_,)
Names of features seen during fit. Defined only when X has feature names that are all strings.
Added in version 1.0.
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)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_
np.float64(0.0195)
See also Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood and Ledoit-Wolf vs OAS estimation for more detailed examples.
Compute the Mean Squared Error between two covariance estimators.
The covariance to compare with.
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_).
If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
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.
The Mean Squared Error (in the sense of the Frobenius norm) between self and comp_cov covariance estimators.
Fit the Oracle Approximating Shrinkage covariance model to X.
Training data, where n_samples is the number of samples and n_features is the number of features.
Not used, present for API consistency by convention.
Returns the instance itself.
Get metadata routing of this object.
Please check User Guide on how the routing mechanism works.
A MetadataRequest encapsulating routing information.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Getter for the precision matrix.
The precision matrix associated to the current covariance object.
Compute the squared Mahalanobis distances of given observations.
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.
Squared Mahalanobis distances of the observations.
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_.
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).
Not used, present for API consistency by convention.
The log-likelihood of X_test with self.location_ and self.covariance_ as estimators of the Gaussian model mean and covariance matrix respectively.
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.
Estimator parameters.
Estimator instance.
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