sklearn.covariance
.OAS¶
- class sklearn.covariance.OAS(*, store_precision=True, assume_centered=False)[source]¶
Oracle Approximating Shrinkage Estimator
Read more in the User Guide.
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. In the original article, formula (23) states that 2/p 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.
- Parameters
- store_precisionbool, default=True
Specify if the estimated precision is stored.
- assume_centeredbool, default=False
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.
- Attributes
- covariance_ndarray of shape (n_features, n_features)
Estimated covariance matrix.
- location_ndarray of shape (n_features,)
Estimated location, i.e. the estimated mean.
- precision_ndarray of shape (n_features, n_features)
Estimated pseudo inverse matrix. (stored only if store_precision is True)
- shrinkage_float
coefficient in the convex combination used for the computation of the shrunk estimate. Range is [0, 1].
- n_features_in_int
Number of features seen during fit.
New in version 0.24.
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])Computes the Mean Squared Error between two covariance estimators.
fit
(X[, y])Fit the Oracle Approximating Shrinkage covariance model according to the given training data and parameters.
get_params
([deep])Get parameters for this estimator.
Getter for the precision matrix.
mahalanobis
(X)Computes the squared Mahalanobis distances of given observations.
score
(X_test[, y])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 this estimator.
- error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)[source]¶
Computes the Mean Squared Error between two covariance estimators. (In the sense of the Frobenius norm).
- 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
andcomp_cov
covariance estimators.
- fit(X, y=None)[source]¶
Fit the Oracle Approximating Shrinkage covariance model according to the given training data and parameters.
- Parameters
- Xarray-like of shape (n_samples, n_features)
Training data, where
n_samples
is the number of samples andn_features
is the number of features.- yIgnored
Not used, present for API consistency by convention.
- Returns
- selfobject
- 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]¶
Computes 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]¶
Computes the log-likelihood of a Gaussian data set with
self.covariance_
as an estimator of its covariance matrix.- 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 likelihood of the data set with
self.covariance_
as an estimator of its covariance matrix.
- 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.