multioutput.py

"""
This module implements multioutput regression and classification.

The estimators provided in this module are meta-estimators: they require
a base estimator to be provided in their constructor. The meta-estimator
extends single output estimators to multioutput estimators.
"""

# Author: Tim Head <betatim@gmail.com>
# Author: Hugo Bowne-Anderson <hugobowne@gmail.com>
# Author: Chris Rivera <chris.richard.rivera@gmail.com>
# Author: Michael Williamson
# Author: James Ashton Nichols <james.ashton.nichols@gmail.com>
#
# License: BSD 3 clause

import numpy as np
import scipy.sparse as sp
from joblib import Parallel

from abc import ABCMeta, abstractmethod
from .base import BaseEstimator, clone, MetaEstimatorMixin
from .base import RegressorMixin, ClassifierMixin, is_classifier
from .model_selection import cross_val_predict
from .utils import check_array, check_X_y, check_random_state
from .utils.metaestimators import if_delegate_has_method
from .utils.validation import (check_is_fitted, has_fit_parameter,
                               _check_fit_params, _deprecate_positional_args)
from .utils.multiclass import check_classification_targets
from .utils.fixes import delayed

__all__ = ["MultiOutputRegressor", "MultiOutputClassifier",
           "ClassifierChain", "RegressorChain"]


def _fit_estimator(estimator, X, y, sample_weight=None, **fit_params):
    estimator = clone(estimator)
    if sample_weight is not None:
        estimator.fit(X, y, sample_weight=sample_weight, **fit_params)
    else:
        estimator.fit(X, y, **fit_params)
    return estimator


def _partial_fit_estimator(estimator, X, y, classes=None, sample_weight=None,
                           first_time=True):
    if first_time:
        estimator = clone(estimator)

    if sample_weight is not None:
        if classes is not None:
            estimator.partial_fit(X, y, classes=classes,
                                  sample_weight=sample_weight)
        else:
            estimator.partial_fit(X, y, sample_weight=sample_weight)
    else:
        if classes is not None:
            estimator.partial_fit(X, y, classes=classes)
        else:
            estimator.partial_fit(X, y)
    return estimator


class _MultiOutputEstimator(MetaEstimatorMixin,
                            BaseEstimator,
                            metaclass=ABCMeta):
    @abstractmethod
    @_deprecate_positional_args
    def __init__(self, estimator, *, n_jobs=None):
        self.estimator = estimator
        self.n_jobs = n_jobs

    @if_delegate_has_method('estimator')
    def partial_fit(self, X, y, classes=None, sample_weight=None):
        """Incrementally fit the model to data.
        Fit a separate model for each output variable.

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

        y : {array-like, sparse matrix} of shape (n_samples, n_outputs)
            Multi-output targets.

        classes : list of ndarray of shape (n_outputs,)
            Each array is unique classes for one output in str/int
            Can be obtained by via
            ``[np.unique(y[:, i]) for i in range(y.shape[1])]``, where y is the
            target matrix of the entire dataset.
            This argument is required for the first call to partial_fit
            and can be omitted in the subsequent calls.
            Note that y doesn't need to contain all labels in `classes`.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted.
            Only supported if the underlying regressor supports sample
            weights.

        Returns
        -------
        self : object
        """
        X, y = check_X_y(X, y,
                         force_all_finite=False,
                         multi_output=True,
                         accept_sparse=True)

        if y.ndim == 1:
            raise ValueError("y must have at least two dimensions for "
                             "multi-output regression but has only one.")

        if (sample_weight is not None and
                not has_fit_parameter(self.estimator, 'sample_weight')):
            raise ValueError("Underlying estimator does not support"
                             " sample weights.")

        first_time = not hasattr(self, 'estimators_')

        self.estimators_ = Parallel(n_jobs=self.n_jobs)(
            delayed(_partial_fit_estimator)(
                self.estimators_[i] if not first_time else self.estimator,
                X, y[:, i],
                classes[i] if classes is not None else None,
                sample_weight, first_time) for i in range(y.shape[1]))
        return self

    def fit(self, X, y, sample_weight=None, **fit_params):
        """ Fit the model to data.
        Fit a separate model for each output variable.

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

        y : {array-like, sparse matrix} of shape (n_samples, n_outputs)
            Multi-output targets. An indicator matrix turns on multilabel
            estimation.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted.
            Only supported if the underlying regressor supports sample
            weights.

        **fit_params : dict of string -> object
            Parameters passed to the ``estimator.fit`` method of each step.

            .. versionadded:: 0.23

        Returns
        -------
        self : object
        """

        if not hasattr(self.estimator, "fit"):
            raise ValueError("The base estimator should implement"
                             " a fit method")

        X, y = self._validate_data(X, y,
                                   force_all_finite=False,
                                   multi_output=True, accept_sparse=True)

        if is_classifier(self):
            check_classification_targets(y)

        if y.ndim == 1:
            raise ValueError("y must have at least two dimensions for "
                             "multi-output regression but has only one.")

        if (sample_weight is not None and
                not has_fit_parameter(self.estimator, 'sample_weight')):
            raise ValueError("Underlying estimator does not support"
                             " sample weights.")

        fit_params_validated = _check_fit_params(X, fit_params)

        self.estimators_ = Parallel(n_jobs=self.n_jobs)(
            delayed(_fit_estimator)(
                self.estimator, X, y[:, i], sample_weight,
                **fit_params_validated)
            for i in range(y.shape[1]))
        return self

    def predict(self, X):
        """Predict multi-output variable using a model
         trained for each target variable.

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

        Returns
        -------
        y : {array-like, sparse matrix} of shape (n_samples, n_outputs)
            Multi-output targets predicted across multiple predictors.
            Note: Separate models are generated for each predictor.
        """
        check_is_fitted(self)
        if not hasattr(self.estimator, "predict"):
            raise ValueError("The base estimator should implement"
                             " a predict method")

        X = check_array(X, force_all_finite=False, accept_sparse=True)

        y = Parallel(n_jobs=self.n_jobs)(
            delayed(e.predict)(X)
            for e in self.estimators_)

        return np.asarray(y).T

    def _more_tags(self):
        return {'multioutput_only': True}


class MultiOutputRegressor(RegressorMixin, _MultiOutputEstimator):
    """Multi target regression

    This strategy consists of fitting one regressor per target. This is a
    simple strategy for extending regressors that do not natively support
    multi-target regression.

    .. versionadded:: 0.18

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing :term:`fit` and :term:`predict`.

    n_jobs : int or None, optional (default=None)
        The number of jobs to run in parallel.
        :meth:`fit`, :meth:`predict` and :meth:`partial_fit` (if supported
        by the passed estimator) will be parallelized for each target.

        When individual estimators are fast to train or predict,
        using ``n_jobs > 1`` can result in slower performance due
        to the parallelism overhead.

        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all available processes / threads.
        See :term:`Glossary <n_jobs>` for more details.

        .. versionchanged:: 0.20
           `n_jobs` default changed from 1 to None

    Attributes
    ----------
    estimators_ : list of ``n_output`` estimators
        Estimators used for predictions.

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.datasets import load_linnerud
    >>> from sklearn.multioutput import MultiOutputRegressor
    >>> from sklearn.linear_model import Ridge
    >>> X, y = load_linnerud(return_X_y=True)
    >>> clf = MultiOutputRegressor(Ridge(random_state=123)).fit(X, y)
    >>> clf.predict(X[[0]])
    array([[176..., 35..., 57...]])
    """
    @_deprecate_positional_args
    def __init__(self, estimator, *, n_jobs=None):
        super().__init__(estimator, n_jobs=n_jobs)

    @if_delegate_has_method('estimator')
    def partial_fit(self, X, y, sample_weight=None):
        """Incrementally fit the model to data.
        Fit a separate model for each output variable.

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

        y : {array-like, sparse matrix} of shape (n_samples, n_outputs)
            Multi-output targets.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted.
            Only supported if the underlying regressor supports sample
            weights.

        Returns
        -------
        self : object
        """
        super().partial_fit(
            X, y, sample_weight=sample_weight)


class MultiOutputClassifier(ClassifierMixin, _MultiOutputEstimator):
    """Multi target classification

    This strategy consists of fitting one classifier per target. This is a
    simple strategy for extending classifiers that do not natively support
    multi-target classification

    Parameters
    ----------
    estimator : estimator object
        An estimator object implementing :term:`fit`, :term:`score` and
        :term:`predict_proba`.

    n_jobs : int or None, optional (default=None)
        The number of jobs to run in parallel.
        :meth:`fit`, :meth:`predict` and :meth:`partial_fit` (if supported
        by the passed estimator) will be parallelized for each target.

        When individual estimators are fast to train or predict,
        using ``n_jobs > 1`` can result in slower performance due
        to the parallelism overhead.

        ``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
        ``-1`` means using all available processes / threads.
        See :term:`Glossary <n_jobs>` for more details.

        .. versionchanged:: 0.20
           `n_jobs` default changed from 1 to None

    Attributes
    ----------
    classes_ : ndarray of shape (n_classes,)
        Class labels.

    estimators_ : list of ``n_output`` estimators
        Estimators used for predictions.

    Examples
    --------
    >>> import numpy as np
    >>> from sklearn.datasets import make_multilabel_classification
    >>> from sklearn.multioutput import MultiOutputClassifier
    >>> from sklearn.neighbors import KNeighborsClassifier

    >>> X, y = make_multilabel_classification(n_classes=3, random_state=0)
    >>> clf = MultiOutputClassifier(KNeighborsClassifier()).fit(X, y)
    >>> clf.predict(X[-2:])
    array([[1, 1, 0], [1, 1, 1]])
    """
    @_deprecate_positional_args
    def __init__(self, estimator, *, n_jobs=None):
        super().__init__(estimator, n_jobs=n_jobs)

    def fit(self, X, Y, sample_weight=None, **fit_params):
        """Fit the model to data matrix X and targets Y.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input data.
        Y : array-like of shape (n_samples, n_classes)
            The target values.
        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted.
            Only supported if the underlying classifier supports sample
            weights.
        **fit_params : dict of string -> object
            Parameters passed to the ``estimator.fit`` method of each step.

            .. versionadded:: 0.23

        Returns
        -------
        self : object
        """
        super().fit(X, Y, sample_weight, **fit_params)
        self.classes_ = [estimator.classes_ for estimator in self.estimators_]
        return self

    @property
    def predict_proba(self):
        """Probability estimates.
        Returns prediction probabilities for each class of each output.

        This method will raise a ``ValueError`` if any of the
        estimators do not have ``predict_proba``.

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

        Returns
        -------
        p : array of shape (n_samples, n_classes), or a list of n_outputs \
            such arrays if n_outputs > 1.
            The class probabilities of the input samples. The order of the
            classes corresponds to that in the attribute :term:`classes_`.

            .. versionchanged:: 0.19
                This function now returns a list of arrays where the length of
                the list is ``n_outputs``, and each array is (``n_samples``,
                ``n_classes``) for that particular output.
        """
        check_is_fitted(self)
        if not all([hasattr(estimator, "predict_proba")
                    for estimator in self.estimators_]):
            raise AttributeError("The base estimator should "
                                 "implement predict_proba method")
        return self._predict_proba

    def _predict_proba(self, X):
        results = [estimator.predict_proba(X) for estimator in
                   self.estimators_]
        return results

    def score(self, X, y):
        """Returns the mean accuracy on the given test data and labels.

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

        y : array-like of shape (n_samples, n_outputs)
            True values for X

        Returns
        -------
        scores : float
            accuracy_score of self.predict(X) versus y
        """
        check_is_fitted(self)
        n_outputs_ = len(self.estimators_)
        if y.ndim == 1:
            raise ValueError("y must have at least two dimensions for "
                             "multi target classification but has only one")
        if y.shape[1] != n_outputs_:
            raise ValueError("The number of outputs of Y for fit {0} and"
                             " score {1} should be same".
                             format(n_outputs_, y.shape[1]))
        y_pred = self.predict(X)
        return np.mean(np.all(y == y_pred, axis=1))

    def _more_tags(self):
        # FIXME
        return {'_skip_test': True}


class _BaseChain(BaseEstimator, metaclass=ABCMeta):
    @_deprecate_positional_args
    def __init__(self, base_estimator, *, order=None, cv=None,
                 random_state=None):
        self.base_estimator = base_estimator
        self.order = order
        self.cv = cv
        self.random_state = random_state

    @abstractmethod
    def fit(self, X, Y, **fit_params):
        """Fit the model to data matrix X and targets Y.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input data.
        Y : array-like of shape (n_samples, n_classes)
            The target values.
        **fit_params : dict of string -> object
            Parameters passed to the `fit` method of each step.

            .. versionadded:: 0.23

        Returns
        -------
        self : object
        """
        X, Y = self._validate_data(X, Y, multi_output=True, accept_sparse=True)

        random_state = check_random_state(self.random_state)
        check_array(X, accept_sparse=True)
        self.order_ = self.order
        if isinstance(self.order_, tuple):
            self.order_ = np.array(self.order_)

        if self.order_ is None:
            self.order_ = np.array(range(Y.shape[1]))
        elif isinstance(self.order_, str):
            if self.order_ == 'random':
                self.order_ = random_state.permutation(Y.shape[1])
        elif sorted(self.order_) != list(range(Y.shape[1])):
            raise ValueError("invalid order")

        self.estimators_ = [clone(self.base_estimator)
                            for _ in range(Y.shape[1])]

        if self.cv is None:
            Y_pred_chain = Y[:, self.order_]
            if sp.issparse(X):
                X_aug = sp.hstack((X, Y_pred_chain), format='lil')
                X_aug = X_aug.tocsr()
            else:
                X_aug = np.hstack((X, Y_pred_chain))

        elif sp.issparse(X):
            Y_pred_chain = sp.lil_matrix((X.shape[0], Y.shape[1]))
            X_aug = sp.hstack((X, Y_pred_chain), format='lil')

        else:
            Y_pred_chain = np.zeros((X.shape[0], Y.shape[1]))
            X_aug = np.hstack((X, Y_pred_chain))

        del Y_pred_chain

        for chain_idx, estimator in enumerate(self.estimators_):
            y = Y[:, self.order_[chain_idx]]
            estimator.fit(X_aug[:, :(X.shape[1] + chain_idx)], y,
                          **fit_params)
            if self.cv is not None and chain_idx < len(self.estimators_) - 1:
                col_idx = X.shape[1] + chain_idx
                cv_result = cross_val_predict(
                    self.base_estimator, X_aug[:, :col_idx],
                    y=y, cv=self.cv)
                if sp.issparse(X_aug):
                    X_aug[:, col_idx] = np.expand_dims(cv_result, 1)
                else:
                    X_aug[:, col_idx] = cv_result

        return self

    def predict(self, X):
        """Predict on the data matrix X using the ClassifierChain model.

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

        Returns
        -------
        Y_pred : array-like of shape (n_samples, n_classes)
            The predicted values.

        """
        check_is_fitted(self)
        X = check_array(X, accept_sparse=True)
        Y_pred_chain = np.zeros((X.shape[0], len(self.estimators_)))
        for chain_idx, estimator in enumerate(self.estimators_):
            previous_predictions = Y_pred_chain[:, :chain_idx]
            if sp.issparse(X):
                if chain_idx == 0:
                    X_aug = X
                else:
                    X_aug = sp.hstack((X, previous_predictions))
            else:
                X_aug = np.hstack((X, previous_predictions))
            Y_pred_chain[:, chain_idx] = estimator.predict(X_aug)

        inv_order = np.empty_like(self.order_)
        inv_order[self.order_] = np.arange(len(self.order_))
        Y_pred = Y_pred_chain[:, inv_order]

        return Y_pred


class ClassifierChain(MetaEstimatorMixin, ClassifierMixin, _BaseChain):
    """A multi-label model that arranges binary classifiers into a chain.

    Each model makes a prediction in the order specified by the chain using
    all of the available features provided to the model plus the predictions
    of models that are earlier in the chain.

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

    .. versionadded:: 0.19

    Parameters
    ----------
    base_estimator : estimator
        The base estimator from which the classifier chain is built.

    order : array-like of shape (n_outputs,) or 'random', default=None
        If None, the order will be determined by the order of columns in
        the label matrix Y.::

            order = [0, 1, 2, ..., Y.shape[1] - 1]

        The order of the chain can be explicitly set by providing a list of
        integers. For example, for a chain of length 5.::

            order = [1, 3, 2, 4, 0]

        means that the first model in the chain will make predictions for
        column 1 in the Y matrix, the second model will make predictions
        for column 3, etc.

        If order is 'random' a random ordering will be used.

    cv : int, cross-validation generator or an iterable, default=None
        Determines whether to use cross validated predictions or true
        labels for the results of previous estimators in the chain.
        Possible inputs for cv are:

        - None, to use true labels when fitting,
        - integer, to specify the number of folds in a (Stratified)KFold,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

    random_state : int, RandomState instance or None, optional (default=None)
        If ``order='random'``, determines random number generation for the
        chain order.
        In addition, it controls the random seed given at each `base_estimator`
        at each chaining iteration. Thus, it is only used when `base_estimator`
        exposes a `random_state`.
        Pass an int for reproducible output across multiple function calls.
        See :term:`Glossary <random_state>`.

    Attributes
    ----------
    classes_ : list
        A list of arrays of length ``len(estimators_)`` containing the
        class labels for each estimator in the chain.

    estimators_ : list
        A list of clones of base_estimator.

    order_ : list
        The order of labels in the classifier chain.

    Examples
    --------
    >>> from sklearn.datasets import make_multilabel_classification
    >>> from sklearn.linear_model import LogisticRegression
    >>> from sklearn.model_selection import train_test_split
    >>> from sklearn.multioutput import ClassifierChain
    >>> X, Y = make_multilabel_classification(
    ...    n_samples=12, n_classes=3, random_state=0
    ... )
    >>> X_train, X_test, Y_train, Y_test = train_test_split(
    ...    X, Y, random_state=0
    ... )
    >>> base_lr = LogisticRegression(solver='lbfgs', random_state=0)
    >>> chain = ClassifierChain(base_lr, order='random', random_state=0)
    >>> chain.fit(X_train, Y_train).predict(X_test)
    array([[1., 1., 0.],
           [1., 0., 0.],
           [0., 1., 0.]])
    >>> chain.predict_proba(X_test)
    array([[0.8387..., 0.9431..., 0.4576...],
           [0.8878..., 0.3684..., 0.2640...],
           [0.0321..., 0.9935..., 0.0625...]])

    See Also
    --------
    RegressorChain : Equivalent for regression.
    MultioutputClassifier : Classifies each output independently rather than
        chaining.

    References
    ----------
    Jesse Read, Bernhard Pfahringer, Geoff Holmes, Eibe Frank, "Classifier
    Chains for Multi-label Classification", 2009.
    """

    def fit(self, X, Y):
        """Fit the model to data matrix X and targets Y.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input data.
        Y : array-like of shape (n_samples, n_classes)
            The target values.

        Returns
        -------
        self : object
        """
        super().fit(X, Y)
        self.classes_ = [estimator.classes_
                         for chain_idx, estimator
                         in enumerate(self.estimators_)]
        return self

    @if_delegate_has_method('base_estimator')
    def predict_proba(self, X):
        """Predict probability estimates.

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

        Returns
        -------
        Y_prob : array-like of shape (n_samples, n_classes)
        """
        X = check_array(X, accept_sparse=True)
        Y_prob_chain = np.zeros((X.shape[0], len(self.estimators_)))
        Y_pred_chain = np.zeros((X.shape[0], len(self.estimators_)))
        for chain_idx, estimator in enumerate(self.estimators_):
            previous_predictions = Y_pred_chain[:, :chain_idx]
            if sp.issparse(X):
                X_aug = sp.hstack((X, previous_predictions))
            else:
                X_aug = np.hstack((X, previous_predictions))
            Y_prob_chain[:, chain_idx] = estimator.predict_proba(X_aug)[:, 1]
            Y_pred_chain[:, chain_idx] = estimator.predict(X_aug)
        inv_order = np.empty_like(self.order_)
        inv_order[self.order_] = np.arange(len(self.order_))
        Y_prob = Y_prob_chain[:, inv_order]

        return Y_prob

    @if_delegate_has_method('base_estimator')
    def decision_function(self, X):
        """Evaluate the decision_function of the models in the chain.

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

        Returns
        -------
        Y_decision : array-like of shape (n_samples, n_classes)
            Returns the decision function of the sample for each model
            in the chain.
        """
        Y_decision_chain = np.zeros((X.shape[0], len(self.estimators_)))
        Y_pred_chain = np.zeros((X.shape[0], len(self.estimators_)))
        for chain_idx, estimator in enumerate(self.estimators_):
            previous_predictions = Y_pred_chain[:, :chain_idx]
            if sp.issparse(X):
                X_aug = sp.hstack((X, previous_predictions))
            else:
                X_aug = np.hstack((X, previous_predictions))
            Y_decision_chain[:, chain_idx] = estimator.decision_function(X_aug)
            Y_pred_chain[:, chain_idx] = estimator.predict(X_aug)

        inv_order = np.empty_like(self.order_)
        inv_order[self.order_] = np.arange(len(self.order_))
        Y_decision = Y_decision_chain[:, inv_order]

        return Y_decision

    def _more_tags(self):
        return {'_skip_test': True,
                'multioutput_only': True}


class RegressorChain(MetaEstimatorMixin, RegressorMixin, _BaseChain):
    """A multi-label model that arranges regressions into a chain.

    Each model makes a prediction in the order specified by the chain using
    all of the available features provided to the model plus the predictions
    of models that are earlier in the chain.

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

    .. versionadded:: 0.20

    Parameters
    ----------
    base_estimator : estimator
        The base estimator from which the classifier chain is built.

    order : array-like of shape (n_outputs,) or 'random', default=None
        If None, the order will be determined by the order of columns in
        the label matrix Y.::

            order = [0, 1, 2, ..., Y.shape[1] - 1]

        The order of the chain can be explicitly set by providing a list of
        integers. For example, for a chain of length 5.::

            order = [1, 3, 2, 4, 0]

        means that the first model in the chain will make predictions for
        column 1 in the Y matrix, the second model will make predictions
        for column 3, etc.

        If order is 'random' a random ordering will be used.

    cv : int, cross-validation generator or an iterable, default=None
        Determines whether to use cross validated predictions or true
        labels for the results of previous estimators in the chain.
        Possible inputs for cv are:

        - None, to use true labels when fitting,
        - integer, to specify the number of folds in a (Stratified)KFold,
        - :term:`CV splitter`,
        - An iterable yielding (train, test) splits as arrays of indices.

    random_state : int, RandomState instance or None, optional (default=None)
        If ``order='random'``, determines random number generation for the
        chain order.
        In addition, it controls the random seed given at each `base_estimator`
        at each chaining iteration. Thus, it is only used when `base_estimator`
        exposes a `random_state`.
        Pass an int for reproducible output across multiple function calls.
        See :term:`Glossary <random_state>`.

    Attributes
    ----------
    estimators_ : list
        A list of clones of base_estimator.

    order_ : list
        The order of labels in the classifier chain.

    Examples
    --------
    >>> from sklearn.multioutput import RegressorChain
    >>> from sklearn.linear_model import LogisticRegression
    >>> logreg = LogisticRegression(solver='lbfgs',multi_class='multinomial')
    >>> X, Y = [[1, 0], [0, 1], [1, 1]], [[0, 2], [1, 1], [2, 0]]
    >>> chain = RegressorChain(base_estimator=logreg, order=[0, 1]).fit(X, Y)
    >>> chain.predict(X)
    array([[0., 2.],
           [1., 1.],
           [2., 0.]])

    See Also
    --------
    ClassifierChain : Equivalent for classification.
    MultioutputRegressor : Learns each output independently rather than
        chaining.

    """

    def fit(self, X, Y, **fit_params):
        """Fit the model to data matrix X and targets Y.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input data.
        Y : array-like of shape (n_samples, n_classes)
            The target values.

        **fit_params : dict of string -> object
            Parameters passed to the `fit` method at each step
            of the regressor chain.

            .. versionadded:: 0.23

        Returns
        -------
        self : object
        """
        super().fit(X, Y, **fit_params)
        return self

    def _more_tags(self):
        return {'multioutput_only': True}