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# `sklearn.covariance`.EmpiricalCovariance

class sklearn.covariance.EmpiricalCovariance(*, store_precision=True, assume_centered=False)

  Maximum likelihood covariance estimator.

  Read more in the User Guide.

  Parameters:
    store_precision bool, default=True

      Specifies if the estimated precision is stored.

    assume_centered bool, default=False

      If True, data are not centered before computation. Useful when working with data whose mean is almost, but not exactly zero. If False (default), data are centered before computation.

  Attributes:
    location_ndarray of shape (n_features,)

      Estimated location, i.e. the estimated mean.

    covariance_ndarray of shape (n_features, n_features)

      Estimated covariance matrix

    precision_ndarray of shape (n_features, n_features)

      Estimated pseudo-inverse matrix. (stored only if store_precision is True)

    n_features_in_int

      Number of features seen during fit.

      New in version 0.24.

    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.

      New in version 1.0.

  See also

  `EllipticEnvelope`

    An object for detecting outliers in a Gaussian distributed dataset.

  `GraphicalLasso`

    Sparse inverse covariance estimation with an l1-penalized estimator.

  `LedoitWolf`

    LedoitWolf Estimator.

  `MinCovDet`

    Minimum Covariance Determinant (robust estimator of covariance).

  `OAS`

    Oracle Approximating Shrinkage Estimator.

  `ShrunkCovariance`

    Covariance estimator with shrinkage.

  Examples

      >>> import numpy as np
      >>> from sklearn.covariance import EmpiricalCovariance
      >>> 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)
      >>> cov = EmpiricalCovariance().fit(X)
      >>> cov.covariance_
      array([[0.7569..., 0.2818...],
             [0.2818..., 0.3928...]])
      >>> cov.location_
      array([0.0622..., 0.0193...])

  Methods

  `error_norm`(comp_cov[, norm, scaling, squared]) | Compute the Mean Squared Error between two covariance estimators.
  `fit`(X[, y]) | Fit the maximum likelihood covariance estimator 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_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.

  fit(X, y=None)

    Fit the maximum likelihood covariance estimator to X.

    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 consistency by convention.

    Returns:
      self object

        Returns the instance itself.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    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 dict

        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:
      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.

  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_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 consistency by convention.

    Returns:
      res float

        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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

  set_score_request(*, X_test: bool | None | str = '$UNCHANGED$') → EmpiricalCovariance

    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.

    New 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_test str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `X_test` parameter in `score`.

    Returns:
      self object

        The updated object.

## Examples using `sklearn.covariance.EmpiricalCovariance`

Robust covariance estimation and Mahalanobis distances relevance

Robust covariance estimation and Mahalanobis distances relevance

Robust vs Empirical covariance estimate

Robust vs Empirical covariance estimate

Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood

Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood