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# `sklearn.linear_model`.MultiTaskLassoCV

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

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

  See glossary entry for cross-validation estimator.

  The optimization objective for MultiTaskLasso is:

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

  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:
    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`.

    copy_X bool, default=True

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

    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.

    verbose bool or int, default=False

      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)

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

    alphas_ndarray of shape (n_alphas,)

      The grid of alphas used for fitting.

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

  `ElasticNetCV`

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

  `MultiTaskElasticNetCV`

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

  Notes

  The algorithm used to fit the model is coordinate descent.

  In `fit`, once the best parameter `alpha` is 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.linear_model import MultiTaskLassoCV
      >>> from sklearn.datasets import make_regression
      >>> from sklearn.metrics import r2_score
      >>> X, y = make_regression(n_targets=2, noise=4, random_state=0)
      >>> reg = MultiTaskLassoCV(cv=5, random_state=0).fit(X, y)
      >>> r2_score(y, reg.predict(X))
      0.9994...
      >>> reg.alpha_
      0.5713...
      >>> reg.predict(X[:1,])
      array([[153.7971...,  94.9015...]])

  Methods

  `fit`(X, y) | Fit MultiTaskLasso model with coordinate descent.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `path`(X, y, *[, eps, n_alphas, alphas, ...]) | Compute Lasso 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 MultiTaskLasso 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)

        Data.

      y ndarray of shape (n_samples, n_targets)

        Target. Will be cast to X’s dtype if necessary.

    Returns:
      self object

        Returns an instance of fitted model.

  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, *, 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, **params)

    Compute Lasso path with coordinate descent.

    The Lasso optimization function varies for mono and multi-outputs.

    For mono-output tasks it is:

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

    For multi-output tasks it is:

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

    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.

      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`).

      **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.

    See also

    `lars_path`

      Compute Least Angle Regression or Lasso path using LARS algorithm.

    `Lasso`

      The Lasso is a linear model that estimates sparse coefficients.

    `LassoLars`

      Lasso model fit with Least Angle Regression a.k.a. Lars.

    `LassoCV`

      Lasso linear model with iterative fitting along a regularization path.

    `LassoLarsCV`

      Cross-validated Lasso using the LARS algorithm.

    `sklearn.decomposition.sparse_encode`

      Estimator that can be used to transform signals into sparse linear combination of atoms from a fixed.

    Notes

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

    To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

    Note that in certain cases, the Lars solver may be significantly faster to implement this functionality. In particular, linear interpolation can be used to retrieve model coefficients between the values output by lars_path

    Examples

    Comparing lasso_path and lars_path with interpolation:

        >>> import numpy as np
        >>> from sklearn.linear_model import lasso_path
        >>> X = np.array([[1, 2, 3.1], [2.3, 5.4, 4.3]]).T
        >>> y = np.array([1, 2, 3.1])
        >>> # Use lasso_path to compute a coefficient path
        >>> _, coef_path, _ = lasso_path(X, y, alphas=[5., 1., .5])
        >>> print(coef_path)
        [[0.         0.         0.46874778]
         [0.2159048  0.4425765  0.23689075]]

        >>> # Now use lars_path and 1D linear interpolation to compute the
        >>> # same path
        >>> from sklearn.linear_model import lars_path
        >>> alphas, active, coef_path_lars = lars_path(X, y, method='lasso')
        >>> from scipy import interpolate
        >>> coef_path_continuous = interpolate.interp1d(alphas[::-1],
        ...                                             coef_path_lars[:, ::-1])
        >>> print(coef_path_continuous([5., 1., .5]))
        [[0.         0.         0.46915237]
         [0.2159048  0.4425765  0.23668876]]

  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 = '$UNCHANGED$') → MultiTaskLassoCV

    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 = '$UNCHANGED$') → MultiTaskLassoCV

    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.