8.2.4. sklearn.covariance.OAS¶
- class sklearn.covariance.OAS(store_precision=True, assume_centered=False)¶
Oracle Approximating Shrinkage Estimator
OAS is a particular form of shrinkage described in “Shrinkage Algorithms for MMSE Covariance Estimation” Chen et al., IEEE Trans. on Sign. Proc., Volume 58, Issue 10, October 2010.
The formula used here does not correspond to the one given in the article. It has been taken from the matlab programm available from the authors webpage (https://tbayes.eecs.umich.edu/yilun/covestimation).
Parameters : store_precision : bool
Specify if the estimated precision is stored
Notes
The regularised covariance is:
(1 - shrinkage)*cov + shrinkage*mu*np.identity(n_features)where mu = trace(cov) / n_features and shinkage 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.
Attributes
covariance_ array-like, shape (n_features, n_features) Estimated covariance matrix precision_ array-like, shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) shrinkage_: float, 0 <= shrinkage <= 1 coefficient in the convex combination used for the computation of the shrunk estimate. Methods
error_norm(comp_cov[, norm, scaling, squared]) Computes the Mean Squared Error between two covariance estimators. fit(X[, assume_centered]) Fits the Oracle Approximating Shrinkage covariance model get_params([deep]) Get parameters for the estimator mahalanobis(observations) Computes the mahalanobis distances of given observations. score(X_test[, assume_centered]) Computes the log-likelihood of a gaussian data set with self.covariance_ as an estimator of its covariance matrix. set_params(**params) Set the parameters of the estimator. - __init__(store_precision=True, assume_centered=False)¶
Parameters : store_precision: bool :
Specify if the estimated precision is stored
assume_centered: Boolean :
If True, data are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False, data are centered before computation.
- error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)¶
Computes the Mean Squared Error between two covariance estimators. (In the sense of the Frobenius norm)
Parameters : comp_cov: array-like, shape = [n_features, n_features] :
The covariance to compare with.
norm: str :
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_).
scaling: bool :
If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
squared: bool :
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 : The Mean Squared Error (in the sense of the Frobenius norm) between :
`self` and `comp_cov` covariance estimators. :
- fit(X, assume_centered=False)¶
Fits the Oracle Approximating Shrinkage covariance model according to the given training data and parameters.
Parameters : X : array-like, shape = [n_samples, n_features]
Training data, where n_samples is the number of samples and n_features is the number of features.
assume_centered: boolean :
If True, data are not centered before computation. Usefull to work with data whose mean is significantly equal to zero but is not exactly zero. If False, data are centered before computation.
Returns : self : object
Returns self.
- get_params(deep=True)¶
Get parameters for the estimator
Parameters : deep: boolean, optional :
If True, will return the parameters for this estimator and contained subobjects that are estimators.
- mahalanobis(observations)¶
Computes the mahalanobis distances of given observations.
The provided observations are assumed to be centered. One may want to center them using a location estimate first.
Parameters : observations: array-like, shape = [n_observations, n_features] :
The observations, the Mahalanobis distances of the which we compute.
Returns : mahalanobis_distance: array, shape = [n_observations,] :
Mahalanobis distances of the observations.
- score(X_test, assume_centered=False)¶
Computes the log-likelihood of a gaussian data set with self.covariance_ as an estimator of its covariance matrix.
Parameters : X_test : array-like, 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.
Returns : res : float
The likelihood of the data set with self.covariance_ as an estimator of its covariance matrix.
- set_params(**params)¶
Set the parameters of the estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.
Returns : self :