`skfolio.moments`.LedoitWolf#

class skfolio.moments.LedoitWolf(store_precision=True, assume_centered=False, block_size=1000, nearest=True, higham=False, higham_max_iteration=100)[source]#

LedoitWolf Covariance Estimator.

Ledoit-Wolf is a particular form of shrinkage, where the shrinkage coefficient is computed using O. Ledoit and M. Wolf’s formula as described in [1].

Read more in scikit-learn.

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.
block_sizeint, default=1000: Size of blocks into which the covariance matrix will be split during its Ledoit-Wolf estimation. This is purely a memory optimization and does not affect results.
nearestbool, default=True: If this is set to True, the covariance is replaced by the nearest covariance matrix that is positive definite and with a Cholesky decomposition than can be computed. The variance is left unchanged. A covariance matrix that is not positive definite often occurs in high dimensional problems. It can be due to multicollinearity, floating-point inaccuracies, or when the number of observations is smaller than the number of assets. For more details, see cov_nearest. The default is True.
highambool, default=False: If this is set to True, the Higham & Nick (2002) algorithm is used to find the nearest PD covariance, otherwise the eigenvalues are clipped to a threshold above zeros (1e-13). The default is False and use the clipping method as the Higham & Nick algorithm can be slow for large datasets.
higham_max_iterationint, default=100: Maximum number of iteration of the Higham & Nick (2002) algorithm. The default value is 100.

Attributes:

covariance_ndarray of shape (n_assets, n_assets): Estimated covariance.
location_ndarray of shape (n_assets,): Estimated location, i.e. the estimated mean.
precision_ndarray of shape (n_assets, n_assets): 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 assets seen during fit.
feature_names_in_ndarray of shape (n_features_in_,): Names of features seen during fit. Defined only when X has feature names that are all strings.

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 Ledoit and Wolf formula (see References)

References

[1]

“A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices”. Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2. February 2004, pages 365-41.

Methods

`error_norm`(comp_cov[, norm, scaling, squared])	Compute the Mean Squared Error between two covariance estimators.
`fit`(X[, y])	Fit the Ledoit-Wolf shrunk covariance model to X.
`get_metadata_routing`()	Get metadata routing of this object.
`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.
`set_score_request`(*[, X_test])	Request metadata passed to the `score` method.

error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)#

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 Ledoit-Wolf shrunk covariance model to X.

Parameters:

Xarray-like of shape (n_observations, n_assets): Price returns of the assets.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfLedoitWolf: Fitted estimator.

get_metadata_routing()#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_params(deep=True)#

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()#

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)#

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)#

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)#

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.

set_score_request(*, X_test='$UNCHANGED$')#

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

X_teststr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for X_test parameter in score.

Returns:

selfobject: The updated object.

skfolio.moments.LedoitWolf#

`skfolio.moments`.LedoitWolf#