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# `sklearn.covariance`.GraphicalLasso

class sklearn.covariance.GraphicalLasso(alpha=0.01, *, mode='cd', covariance=None, tol=0.0001, enet_tol=0.0001, max_iter=100, verbose=False, eps=2.220446049250313e-16, assume_centered=False)

  Sparse inverse covariance estimation with an l1-penalized estimator.

  Read more in the User Guide.

  Changed in version v0.20: GraphLasso has been renamed to GraphicalLasso

  Parameters:
    alpha float, default=0.01

      The regularization parameter: the higher alpha, the more regularization, the sparser the inverse covariance. Range is (0, inf].

    mode{‘cd’, ‘lars’}, default=’cd’

      The Lasso solver to use: coordinate descent or LARS. Use LARS for very sparse underlying graphs, where p > n. Elsewhere prefer cd which is more numerically stable.

    covariance“precomputed”, default=None

      If covariance is “precomputed”, the input data in `fit` is assumed to be the covariance matrix. If `None`, the empirical covariance is estimated from the data `X`.

      New in version 1.3.

    tol float, default=1e-4

      The tolerance to declare convergence: if the dual gap goes below this value, iterations are stopped. Range is (0, inf].

    enet_tol float, default=1e-4

      The tolerance for the elastic net solver used to calculate the descent direction. This parameter controls the accuracy of the search direction for a given column update, not of the overall parameter estimate. Only used for mode=’cd’. Range is (0, inf].

    max_iter int, default=100

      The maximum number of iterations.

    verbose bool, default=False

      If verbose is True, the objective function and dual gap are plotted at each iteration.

    eps float, default=eps

      The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Default is `np.finfo(np.float64).eps`.

      New in version 1.3.

    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, 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.

    n_iter_int

      Number of iterations run.

    costs_list of (objective, dual_gap) pairs

      The list of values of the objective function and the dual gap at each iteration. Returned only if return_costs is True.

      New in version 1.3.

    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

  `graphical_lasso`

    L1-penalized covariance estimator.

  `GraphicalLassoCV`

    Sparse inverse covariance with cross-validated choice of the l1 penalty.

  Examples

      >>> import numpy as np
      >>> from sklearn.covariance import GraphicalLasso
      >>> true_cov = np.array([[0.8, 0.0, 0.2, 0.0],
      ...                      [0.0, 0.4, 0.0, 0.0],
      ...                      [0.2, 0.0, 0.3, 0.1],
      ...                      [0.0, 0.0, 0.1, 0.7]])
      >>> np.random.seed(0)
      >>> X = np.random.multivariate_normal(mean=[0, 0, 0, 0],
      ...                                   cov=true_cov,
      ...                                   size=200)
      >>> cov = GraphicalLasso().fit(X)
      >>> np.around(cov.covariance_, decimals=3)
      array([[0.816, 0.049, 0.218, 0.019],
             [0.049, 0.364, 0.017, 0.034],
             [0.218, 0.017, 0.322, 0.093],
             [0.019, 0.034, 0.093, 0.69 ]])
      >>> np.around(cov.location_, decimals=3)
      array([0.073, 0.04 , 0.038, 0.143])

  Methods

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

    Parameters:
      X array-like of shape (n_samples, n_features)

        Data from which to compute the covariance estimate.

      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 = '$UNCHANGED$') → GraphicalLasso

    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.