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# `sklearn.linear_model`.MultiTaskElasticNetCV

class sklearn.linear_model.MultiTaskElasticNetCV(*, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, fit_intercept=True, max_iter=1000, tol=0.0001, cv=None, copy_X=True, verbose=0, n_jobs=None, random_state=None, selection='cyclic')

  Multi-task L1/L2 ElasticNet with built-in cross-validation.

  See glossary entry for cross-validation estimator.

  The optimization objective for MultiTaskElasticNet is:

      (1 / (2 * n_samples)) * ||Y - XW||^Fro_2
      + alpha * l1_ratio * ||W||_21
      + 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2

  Where:

      ||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

  i.e. the sum of norm of each row.

  Read more in the User Guide.

  New in version 0.15.

  Parameters:
    l1_ratio float or list of float, default=0.5

      The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it is an L2 penalty. For `0 < l1_ratio < 1`, the penalty is a combination of L1/L2 and L2. This parameter can be a list, in which case the different values are tested by cross-validation and the one giving the best prediction score is used. Note that a good choice of list of values for l1_ratio is often to put more values close to 1 (i.e. Lasso) and less close to 0 (i.e. Ridge), as in `[.1, .5, .7, .9, .95, .99, 1]`.

    eps float, default=1e-3

      Length of the path. `eps=1e-3` means that `alpha_min / alpha_max = 1e-3`.

    n_alphas int, default=100

      Number of alphas along the regularization path.

    alphas array-like, default=None

      List of alphas where to compute the models. If not provided, set automatically.

    fit_intercept bool, default=True

      Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).

    max_iter int, default=1000

      The maximum number of iterations.

    tol float, default=1e-4

      The tolerance for the optimization: if the updates are smaller than `tol`, the optimization code checks the dual gap for optimality and continues until it is smaller than `tol`.

    cv int, cross-validation generator or iterable, default=None

      Determines the cross-validation splitting strategy. Possible inputs for cv are:

      - None, to use the default 5-fold cross-validation,

      - int, to specify the number of folds.

      - CV splitter,

      - An iterable yielding (train, test) splits as arrays of indices.

      For int/None inputs, `KFold` is used.

      Refer User Guide for the various cross-validation strategies that can be used here.

      Changed in version 0.22: `cv` default value if None changed from 3-fold to 5-fold.

    copy_X bool, default=True

      If `True`, X will be copied; else, it may be overwritten.

    verbose bool or int, default=0

      Amount of verbosity.

    n_jobs int, default=None

      Number of CPUs to use during the cross validation. Note that this is used only if multiple values for l1_ratio are given. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    random_state int, RandomState instance, default=None

      The seed of the pseudo random number generator that selects a random feature to update. Used when `selection` == ‘random’. Pass an int for reproducible output across multiple function calls. See Glossary.

    selection{‘cyclic’, ‘random’}, default=’cyclic’

      If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

  Attributes:
    intercept_ndarray of shape (n_targets,)

      Independent term in decision function.

    coef_ndarray of shape (n_targets, n_features)

      Parameter vector (W in the cost function formula). Note that `coef_` stores the transpose of `W`, `W.T`.

    alpha_float

      The amount of penalization chosen by cross validation.

    mse_path_ndarray of shape (n_alphas, n_folds) or (n_l1_ratio, n_alphas, n_folds)

      Mean square error for the test set on each fold, varying alpha.

    alphas_ndarray of shape (n_alphas,) or (n_l1_ratio, n_alphas)

      The grid of alphas used for fitting, for each l1_ratio.

    l1_ratio_float

      Best l1_ratio obtained by cross-validation.

    n_iter_int

      Number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

    dual_gap_float

      The dual gap at the end of the optimization for the optimal alpha.

    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

  `MultiTaskElasticNet`

    Multi-task L1/L2 ElasticNet with built-in cross-validation.

  `ElasticNetCV`

    Elastic net model with best model selection by cross-validation.

  `MultiTaskLassoCV`

    Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer.

  Notes

  The algorithm used to fit the model is coordinate descent.

  In `fit`, once the best parameters `l1_ratio` and `alpha` are found through cross-validation, the model is fit again using the entire training set.

  To avoid unnecessary memory duplication the `X` and `y` arguments of the `fit` method should be directly passed as Fortran-contiguous numpy arrays.

  Examples

      >>> from sklearn import linear_model
      >>> clf = linear_model.MultiTaskElasticNetCV(cv=3)
      >>> clf.fit([[0,0], [1, 1], [2, 2]],
      ...         [[0, 0], [1, 1], [2, 2]])
      MultiTaskElasticNetCV(cv=3)
      >>> print(clf.coef_)
      [[0.52875032 0.46958558]
       [0.52875032 0.46958558]]
      >>> print(clf.intercept_)
      [0.00166409 0.00166409]

  Methods

  `fit`(X, y) | Fit MultiTaskElasticNet model with coordinate descent.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `path`(X, y, *[, l1_ratio, eps, n_alphas, ...]) | Compute elastic net path with coordinate descent.
  `predict`(X) | Predict using the linear model.
  `score`(X, y[, sample_weight]) | Return the coefficient of determination of the prediction.
  `set_fit_request`(*[, sample_weight]) | Request metadata passed to the `fit` method.
  `set_params`(**params) | Set the parameters of this estimator.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.

  fit(X, y)

    Fit MultiTaskElasticNet model with coordinate descent.

    Fit is on grid of alphas and best alpha estimated by cross-validation.

    Parameters:
      X ndarray of shape (n_samples, n_features)

        Training data.

      y ndarray of shape (n_samples, n_targets)

        Training target variable. Will be cast to X’s dtype if necessary.

    Returns:
      self object

        Returns MultiTaskElasticNet instance.

  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.

  static path(X, y, *, l1_ratio=0.5, eps=0.001, n_alphas=100, alphas=None, precompute='auto', Xy=None, copy_X=True, coef_init=None, verbose=False, return_n_iter=False, positive=False, check_input=True, **params)

    Compute elastic net path with coordinate descent.

    The elastic net optimization function varies for mono and multi-outputs.

    For mono-output tasks it is:

        1 / (2 * n_samples) * ||y - Xw||^2_2
        + alpha * l1_ratio * ||w||_1
        + 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2

    For multi-output tasks it is:

        (1 / (2 * n_samples)) * ||Y - XW||_Fro^2
        + alpha * l1_ratio * ||W||_21
        + 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2

    Where:

        ||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

    i.e. the sum of norm of each row.

    Read more in the User Guide.

    Parameters:
      X{array-like, sparse matrix} of shape (n_samples, n_features)

        Training data. Pass directly as Fortran-contiguous data to avoid unnecessary memory duplication. If `y` is mono-output then `X` can be sparse.

      y{array-like, sparse matrix} of shape (n_samples,) or (n_samples, n_targets)

        Target values.

      l1_ratio float, default=0.5

        Number between 0 and 1 passed to elastic net (scaling between l1 and l2 penalties). `l1_ratio=1` corresponds to the Lasso.

      eps float, default=1e-3

        Length of the path. `eps=1e-3` means that `alpha_min / alpha_max = 1e-3`.

      n_alphas int, default=100

        Number of alphas along the regularization path.

      alphas ndarray, default=None

        List of alphas where to compute the models. If None alphas are set automatically.

      precompute‘auto’, bool or array-like of shape (n_features, n_features), default=’auto’

        Whether to use a precomputed Gram matrix to speed up calculations. If set to `'auto'` let us decide. The Gram matrix can also be passed as argument.

      Xy array-like of shape (n_features,) or (n_features, n_targets), default=None

        Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.

      copy_X bool, default=True

        If `True`, X will be copied; else, it may be overwritten.

      coef_init ndarray of shape (n_features, ), default=None

        The initial values of the coefficients.

      verbose bool or int, default=False

        Amount of verbosity.

      return_n_iter bool, default=False

        Whether to return the number of iterations or not.

      positive bool, default=False

        If set to True, forces coefficients to be positive. (Only allowed when `y.ndim == 1`).

      check_input bool, default=True

        If set to False, the input validation checks are skipped (including the Gram matrix when provided). It is assumed that they are handled by the caller.

      **params kwargs

        Keyword arguments passed to the coordinate descent solver.

    Returns:
      alphas ndarray of shape (n_alphas,)

        The alphas along the path where models are computed.

      coefs ndarray of shape (n_features, n_alphas) or (n_targets, n_features, n_alphas)

        Coefficients along the path.

      dual_gaps ndarray of shape (n_alphas,)

        The dual gaps at the end of the optimization for each alpha.

      n_iters list of int

        The number of iterations taken by the coordinate descent optimizer to reach the specified tolerance for each alpha. (Is returned when `return_n_iter` is set to True).

    See also

    `MultiTaskElasticNet`

      Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer.

    `MultiTaskElasticNetCV`

      Multi-task L1/L2 ElasticNet with built-in cross-validation.

    `ElasticNet`

      Linear regression with combined L1 and L2 priors as regularizer.

    `ElasticNetCV`

      Elastic Net model with iterative fitting along a regularization path.

    Notes

    For an example, see examples/linear_model/plot_lasso_coordinate_descent_path.py.

  predict(X)

    Predict using the linear model.

    Parameters:
      X array-like or sparse matrix, shape (n_samples, n_features)

        Samples.

    Returns:
      C array, shape (n_samples,)

        Returns predicted values.

  score(X, y, sample_weight=None)

    Return the coefficient of determination of the prediction.

    The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares `((y_true - y_pred)** 2).sum()` and \(v\) is the total sum of squares `((y_true - y_true.mean()) ** 2).sum()`. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of `y`, disregarding the input features, would get a \(R^2\) score of 0.0.

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

        Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape `(n_samples, n_samples_fitted)`, where `n_samples_fitted` is the number of samples used in the fitting for the estimator.

      y array-like of shape (n_samples,) or (n_samples, n_outputs)

        True values for `X`.

      sample_weight array-like of shape (n_samples,), default=None

        Sample weights.

    Returns:
      score float

        \(R^2\) of `self.predict(X)` w.r.t. `y`.

    Notes

    The \(R^2\) score used when calling `score` on a regressor uses `multioutput='uniform_average'` from version 0.23 to keep consistent with default value of `r2_score`. This influences the `score` method of all the multioutput regressors (except for `MultiOutputRegressor`).

  set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → MultiTaskElasticNetCV

    Request metadata passed to the `fit` 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 `fit` 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 `fit`.

    - `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:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `fit`.

    Returns:
      self object

        The updated object.

  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(*, sample_weight: bool | None | str = '$UNCHANGED$') → MultiTaskElasticNetCV

    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:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

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

    Returns:
      self object

        The updated object.