package sklearn

  1. Overview
  2. Docs
package sklearn
Legend:
Library
Module
Module type
Parameter
Class
Class type
type tag = [
  1. | `LedoitWolf
]
type t = [ `BaseEstimator | `LedoitWolf | `Object ] Obj.t
val of_pyobject : Py.Object.t -> t
val to_pyobject : [> tag ] Obj.t -> Py.Object.t
val as_estimator : t -> [ `BaseEstimator ] Obj.t
val create : ?store_precision:bool -> ?assume_centered:bool -> ?block_size:int -> unit -> t

LedoitWolf 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 'A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices', Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411.

Read more in the :ref:`User Guide <shrunk_covariance>`.

Parameters ---------- store_precision : bool, default=True Specify if the estimated precision is stored.

assume_centered : bool, 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_size : int, default=1000 Size of the 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.

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.

Examples -------- >>> import numpy as np >>> from sklearn.covariance import LedoitWolf >>> real_cov = np.array([.4, .2], ... [.2, .8]) >>> np.random.seed(0) >>> X = np.random.multivariate_normal(mean=0, 0, ... cov=real_cov, ... size=50) >>> cov = LedoitWolf().fit(X) >>> cov.covariance_ array([0.4406..., 0.1616...], [0.1616..., 0.8022...]) >>> cov.location_ array( 0.0595... , -0.0075...)

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 ---------- 'A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices', Ledoit and Wolf, Journal of Multivariate Analysis, Volume 88, Issue 2, February 2004, pages 365-411.

val error_norm : ?norm:[ `Frobenius | `Spectral ] -> ?scaling:bool -> ?squared:bool -> comp_cov:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> float

Computes the Mean Squared Error between two covariance estimators. (In the sense of the Frobenius norm).

Parameters ---------- comp_cov : array-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_)``.

scaling : bool, default=True If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.

squared : bool, 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 ------- result : float The Mean Squared Error (in the sense of the Frobenius norm) between `self` and `comp_cov` covariance estimators.

val fit : ?y:Py.Object.t -> x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> t

Fit the Ledoit-Wolf shrunk covariance model according to the given training data and parameters.

Parameters ---------- X : array-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. y : Ignored not used, present for API consistence purpose.

Returns ------- self : object

val get_params : ?deep:bool -> [> tag ] Obj.t -> Dict.t

Get parameters for this estimator.

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

Returns ------- params : mapping of string to any Parameter names mapped to their values.

val get_precision : [> tag ] Obj.t -> [> `ArrayLike ] Np.Obj.t

Getter for the precision matrix.

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

val mahalanobis : x:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> [> `ArrayLike ] Np.Obj.t

Computes the squared Mahalanobis distances of given observations.

Parameters ---------- X : array-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 ------- dist : ndarray of shape (n_samples,) Squared Mahalanobis distances of the observations.

val score : ?y:Py.Object.t -> x_test:[> `ArrayLike ] Np.Obj.t -> [> tag ] Obj.t -> float

Computes the log-likelihood of a Gaussian data set with `self.covariance_` as an estimator of its covariance matrix.

Parameters ---------- X_test : array-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).

y : Ignored Not used, present for API consistence purpose.

Returns ------- res : float The likelihood of the data set with `self.covariance_` as an estimator of its covariance matrix.

val set_params : ?params:(string * Py.Object.t) list -> [> tag ] Obj.t -> t

Set the parameters of this estimator.

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

Parameters ---------- **params : dict Estimator parameters.

Returns ------- self : object Estimator instance.

val covariance_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute covariance_: get value or raise Not_found if None.

val covariance_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute covariance_: get value as an option.

val location_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute location_: get value or raise Not_found if None.

val location_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute location_: get value as an option.

val precision_ : t -> [> `ArrayLike ] Np.Obj.t

Attribute precision_: get value or raise Not_found if None.

val precision_opt : t -> [> `ArrayLike ] Np.Obj.t option

Attribute precision_: get value as an option.

val shrinkage_ : t -> float

Attribute shrinkage_: get value or raise Not_found if None.

val shrinkage_opt : t -> float option

Attribute shrinkage_: get value as an option.

val to_string : t -> string

Print the object to a human-readable representation.

val show : t -> string

Print the object to a human-readable representation.

val pp : Stdlib.Format.formatter -> t -> unit

Pretty-print the object to a formatter.