_classes.py

"""
This module gathers tree-based methods, including decision, regression and
randomized trees. Single and multi-output problems are both handled.
"""

# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause

import copy
import numbers
from abc import ABCMeta, abstractmethod
from math import ceil
from numbers import Integral, Real

import numpy as np
from scipy.sparse import issparse

from sklearn.utils import metadata_routing

from ..base import (
    BaseEstimator,
    ClassifierMixin,
    MultiOutputMixin,
    RegressorMixin,
    _fit_context,
    clone,
    is_classifier,
)
from ..utils import Bunch, check_random_state, compute_sample_weight
from ..utils._param_validation import Hidden, Interval, RealNotInt, StrOptions
from ..utils.multiclass import check_classification_targets
from ..utils.validation import (
    _assert_all_finite_element_wise,
    _check_n_features,
    _check_sample_weight,
    assert_all_finite,
    check_is_fitted,
    validate_data,
)
from . import _criterion, _splitter, _tree
from ._criterion import Criterion
from ._splitter import Splitter
from ._tree import (
    BestFirstTreeBuilder,
    DepthFirstTreeBuilder,
    Tree,
    _build_pruned_tree_ccp,
    ccp_pruning_path,
)
from ._utils import _any_isnan_axis0

__all__ = [
    "DecisionTreeClassifier",
    "DecisionTreeRegressor",
    "ExtraTreeClassifier",
    "ExtraTreeRegressor",
]


# =============================================================================
# Types and constants
# =============================================================================

DTYPE = _tree.DTYPE
DOUBLE = _tree.DOUBLE

CRITERIA_CLF = {
    "gini": _criterion.Gini,
    "log_loss": _criterion.Entropy,
    "entropy": _criterion.Entropy,
}
CRITERIA_REG = {
    "squared_error": _criterion.MSE,
    "friedman_mse": _criterion.FriedmanMSE,
    "absolute_error": _criterion.MAE,
    "poisson": _criterion.Poisson,
}

DENSE_SPLITTERS = {"best": _splitter.BestSplitter, "random": _splitter.RandomSplitter}

SPARSE_SPLITTERS = {
    "best": _splitter.BestSparseSplitter,
    "random": _splitter.RandomSparseSplitter,
}

# =============================================================================
# Base decision tree
# =============================================================================


class BaseDecisionTree(MultiOutputMixin, BaseEstimator, metaclass=ABCMeta):
    """Base class for decision trees.

    Warning: This class should not be used directly.
    Use derived classes instead.
    """

    # "check_input" is used for optimisation and isn't something to be passed
    # around in a pipeline.
    __metadata_request__predict = {"check_input": metadata_routing.UNUSED}

    _parameter_constraints: dict = {
        "splitter": [StrOptions({"best", "random"})],
        "max_depth": [Interval(Integral, 1, None, closed="left"), None],
        "min_samples_split": [
            Interval(Integral, 2, None, closed="left"),
            Interval(RealNotInt, 0.0, 1.0, closed="right"),
        ],
        "min_samples_leaf": [
            Interval(Integral, 1, None, closed="left"),
            Interval(RealNotInt, 0.0, 1.0, closed="neither"),
        ],
        "min_weight_fraction_leaf": [Interval(Real, 0.0, 0.5, closed="both")],
        "max_features": [
            Interval(Integral, 1, None, closed="left"),
            Interval(RealNotInt, 0.0, 1.0, closed="right"),
            StrOptions({"sqrt", "log2"}),
            None,
        ],
        "random_state": ["random_state"],
        "max_leaf_nodes": [Interval(Integral, 2, None, closed="left"), None],
        "min_impurity_decrease": [Interval(Real, 0.0, None, closed="left")],
        "ccp_alpha": [Interval(Real, 0.0, None, closed="left")],
        "monotonic_cst": ["array-like", None],
    }

    @abstractmethod
    def __init__(
        self,
        *,
        criterion,
        splitter,
        max_depth,
        min_samples_split,
        min_samples_leaf,
        min_weight_fraction_leaf,
        max_features,
        max_leaf_nodes,
        random_state,
        min_impurity_decrease,
        class_weight=None,
        ccp_alpha=0.0,
        monotonic_cst=None,
    ):
        self.criterion = criterion
        self.splitter = splitter
        self.max_depth = max_depth
        self.min_samples_split = min_samples_split
        self.min_samples_leaf = min_samples_leaf
        self.min_weight_fraction_leaf = min_weight_fraction_leaf
        self.max_features = max_features
        self.max_leaf_nodes = max_leaf_nodes
        self.random_state = random_state
        self.min_impurity_decrease = min_impurity_decrease
        self.class_weight = class_weight
        self.ccp_alpha = ccp_alpha
        self.monotonic_cst = monotonic_cst

    def get_depth(self):
        """Return the depth of the decision tree.

        The depth of a tree is the maximum distance between the root
        and any leaf.

        Returns
        -------
        self.tree_.max_depth : int
            The maximum depth of the tree.
        """
        check_is_fitted(self)
        return self.tree_.max_depth

    def get_n_leaves(self):
        """Return the number of leaves of the decision tree.

        Returns
        -------
        self.tree_.n_leaves : int
            Number of leaves.
        """
        check_is_fitted(self)
        return self.tree_.n_leaves

    def _support_missing_values(self, X):
        return (
            not issparse(X)
            and self.__sklearn_tags__().input_tags.allow_nan
            and self.monotonic_cst is None
        )

    def _compute_missing_values_in_feature_mask(self, X, estimator_name=None):
        """Return boolean mask denoting if there are missing values for each feature.

        This method also ensures that X is finite.

        Parameter
        ---------
        X : array-like of shape (n_samples, n_features), dtype=DOUBLE
            Input data.

        estimator_name : str or None, default=None
            Name to use when raising an error. Defaults to the class name.

        Returns
        -------
        missing_values_in_feature_mask : ndarray of shape (n_features,), or None
            Missing value mask. If missing values are not supported or there
            are no missing values, return None.
        """
        estimator_name = estimator_name or self.__class__.__name__
        common_kwargs = dict(estimator_name=estimator_name, input_name="X")

        if not self._support_missing_values(X):
            assert_all_finite(X, **common_kwargs)
            return None

        with np.errstate(over="ignore"):
            overall_sum = np.sum(X)

        if not np.isfinite(overall_sum):
            # Raise a ValueError in case of the presence of an infinite element.
            _assert_all_finite_element_wise(X, xp=np, allow_nan=True, **common_kwargs)

        # If the sum is not nan, then there are no missing values
        if not np.isnan(overall_sum):
            return None

        missing_values_in_feature_mask = _any_isnan_axis0(X)
        return missing_values_in_feature_mask

    def _fit(
        self,
        X,
        y,
        sample_weight=None,
        check_input=True,
        missing_values_in_feature_mask=None,
    ):
        random_state = check_random_state(self.random_state)

        if check_input:
            # Need to validate separately here.
            # We can't pass multi_output=True because that would allow y to be
            # csr.

            # _compute_missing_values_in_feature_mask will check for finite values and
            # compute the missing mask if the tree supports missing values
            check_X_params = dict(
                dtype=DTYPE, accept_sparse="csc", ensure_all_finite=False
            )
            check_y_params = dict(ensure_2d=False, dtype=None)
            X, y = validate_data(
                self, X, y, validate_separately=(check_X_params, check_y_params)
            )

            missing_values_in_feature_mask = (
                self._compute_missing_values_in_feature_mask(X)
            )
            if issparse(X):
                X.sort_indices()

                if X.indices.dtype != np.intc or X.indptr.dtype != np.intc:
                    raise ValueError(
                        "No support for np.int64 index based sparse matrices"
                    )

            if self.criterion == "poisson":
                if np.any(y < 0):
                    raise ValueError(
                        "Some value(s) of y are negative which is"
                        " not allowed for Poisson regression."
                    )
                if np.sum(y) <= 0:
                    raise ValueError(
                        "Sum of y is not positive which is "
                        "necessary for Poisson regression."
                    )

        # Determine output settings
        n_samples, self.n_features_in_ = X.shape
        is_classification = is_classifier(self)

        y = np.atleast_1d(y)
        expanded_class_weight = None

        if y.ndim == 1:
            # reshape is necessary to preserve the data contiguity against vs
            # [:, np.newaxis] that does not.
            y = np.reshape(y, (-1, 1))

        self.n_outputs_ = y.shape[1]

        if is_classification:
            check_classification_targets(y)
            y = np.copy(y)

            self.classes_ = []
            self.n_classes_ = []

            if self.class_weight is not None:
                y_original = np.copy(y)

            y_encoded = np.zeros(y.shape, dtype=int)
            for k in range(self.n_outputs_):
                classes_k, y_encoded[:, k] = np.unique(y[:, k], return_inverse=True)
                self.classes_.append(classes_k)
                self.n_classes_.append(classes_k.shape[0])
            y = y_encoded

            if self.class_weight is not None:
                expanded_class_weight = compute_sample_weight(
                    self.class_weight, y_original
                )

            self.n_classes_ = np.array(self.n_classes_, dtype=np.intp)

        if getattr(y, "dtype", None) != DOUBLE or not y.flags.contiguous:
            y = np.ascontiguousarray(y, dtype=DOUBLE)

        max_depth = np.iinfo(np.int32).max if self.max_depth is None else self.max_depth

        if isinstance(self.min_samples_leaf, numbers.Integral):
            min_samples_leaf = self.min_samples_leaf
        else:  # float
            min_samples_leaf = ceil(self.min_samples_leaf * n_samples)

        if isinstance(self.min_samples_split, numbers.Integral):
            min_samples_split = self.min_samples_split
        else:  # float
            min_samples_split = ceil(self.min_samples_split * n_samples)
            min_samples_split = max(2, min_samples_split)

        min_samples_split = max(min_samples_split, 2 * min_samples_leaf)

        if isinstance(self.max_features, str):
            if self.max_features == "sqrt":
                max_features = max(1, int(np.sqrt(self.n_features_in_)))
            elif self.max_features == "log2":
                max_features = max(1, int(np.log2(self.n_features_in_)))
        elif self.max_features is None:
            max_features = self.n_features_in_
        elif isinstance(self.max_features, numbers.Integral):
            max_features = self.max_features
        else:  # float
            if self.max_features > 0.0:
                max_features = max(1, int(self.max_features * self.n_features_in_))
            else:
                max_features = 0

        self.max_features_ = max_features

        max_leaf_nodes = -1 if self.max_leaf_nodes is None else self.max_leaf_nodes

        if len(y) != n_samples:
            raise ValueError(
                "Number of labels=%d does not match number of samples=%d"
                % (len(y), n_samples)
            )

        if sample_weight is not None:
            sample_weight = _check_sample_weight(sample_weight, X, dtype=DOUBLE)

        if expanded_class_weight is not None:
            if sample_weight is not None:
                sample_weight = sample_weight * expanded_class_weight
            else:
                sample_weight = expanded_class_weight

        # Set min_weight_leaf from min_weight_fraction_leaf
        if sample_weight is None:
            min_weight_leaf = self.min_weight_fraction_leaf * n_samples
        else:
            min_weight_leaf = self.min_weight_fraction_leaf * np.sum(sample_weight)

        # Build tree
        criterion = self.criterion
        if not isinstance(criterion, Criterion):
            if is_classification:
                criterion = CRITERIA_CLF[self.criterion](
                    self.n_outputs_, self.n_classes_
                )
            else:
                criterion = CRITERIA_REG[self.criterion](self.n_outputs_, n_samples)
        else:
            # Make a deepcopy in case the criterion has mutable attributes that
            # might be shared and modified concurrently during parallel fitting
            criterion = copy.deepcopy(criterion)

        SPLITTERS = SPARSE_SPLITTERS if issparse(X) else DENSE_SPLITTERS

        splitter = self.splitter
        if self.monotonic_cst is None:
            monotonic_cst = None
        else:
            if self.n_outputs_ > 1:
                raise ValueError(
                    "Monotonicity constraints are not supported with multiple outputs."
                )
            # Check to correct monotonicity constraint' specification,
            # by applying element-wise logical conjunction
            # Note: we do not cast `np.asarray(self.monotonic_cst, dtype=np.int8)`
            # straight away here so as to generate error messages for invalid
            # values using the original values prior to any dtype related conversion.
            monotonic_cst = np.asarray(self.monotonic_cst)
            if monotonic_cst.shape[0] != X.shape[1]:
                raise ValueError(
                    "monotonic_cst has shape {} but the input data "
                    "X has {} features.".format(monotonic_cst.shape[0], X.shape[1])
                )
            valid_constraints = np.isin(monotonic_cst, (-1, 0, 1))
            if not np.all(valid_constraints):
                unique_constaints_value = np.unique(monotonic_cst)
                raise ValueError(
                    "monotonic_cst must be None or an array-like of -1, 0 or 1, but"
                    f" got {unique_constaints_value}"
                )
            monotonic_cst = np.asarray(monotonic_cst, dtype=np.int8)
            if is_classifier(self):
                if self.n_classes_[0] > 2:
                    raise ValueError(
                        "Monotonicity constraints are not supported with multiclass "
                        "classification"
                    )
                # Binary classification trees are built by constraining probabilities
                # of the *negative class* in order to make the implementation similar
                # to regression trees.
                # Since self.monotonic_cst encodes constraints on probabilities of the
                # *positive class*, all signs must be flipped.
                monotonic_cst *= -1

        if not isinstance(self.splitter, Splitter):
            splitter = SPLITTERS[self.splitter](
                criterion,
                self.max_features_,
                min_samples_leaf,
                min_weight_leaf,
                random_state,
                monotonic_cst,
            )

        if is_classifier(self):
            self.tree_ = Tree(self.n_features_in_, self.n_classes_, self.n_outputs_)
        else:
            self.tree_ = Tree(
                self.n_features_in_,
                # TODO: tree shouldn't need this in this case
                np.array([1] * self.n_outputs_, dtype=np.intp),
                self.n_outputs_,
            )

        # Use BestFirst if max_leaf_nodes given; use DepthFirst otherwise
        if max_leaf_nodes < 0:
            builder = DepthFirstTreeBuilder(
                splitter,
                min_samples_split,
                min_samples_leaf,
                min_weight_leaf,
                max_depth,
                self.min_impurity_decrease,
            )
        else:
            builder = BestFirstTreeBuilder(
                splitter,
                min_samples_split,
                min_samples_leaf,
                min_weight_leaf,
                max_depth,
                max_leaf_nodes,
                self.min_impurity_decrease,
            )

        builder.build(self.tree_, X, y, sample_weight, missing_values_in_feature_mask)

        if self.n_outputs_ == 1 and is_classifier(self):
            self.n_classes_ = self.n_classes_[0]
            self.classes_ = self.classes_[0]

        self._prune_tree()

        return self

    def _validate_X_predict(self, X, check_input):
        """Validate the training data on predict (probabilities)."""
        if check_input:
            if self._support_missing_values(X):
                ensure_all_finite = "allow-nan"
            else:
                ensure_all_finite = True
            X = validate_data(
                self,
                X,
                dtype=DTYPE,
                accept_sparse="csr",
                reset=False,
                ensure_all_finite=ensure_all_finite,
            )
            if issparse(X) and (
                X.indices.dtype != np.intc or X.indptr.dtype != np.intc
            ):
                raise ValueError("No support for np.int64 index based sparse matrices")
        else:
            # The number of features is checked regardless of `check_input`
            _check_n_features(self, X, reset=False)
        return X

    def predict(self, X, check_input=True):
        """Predict class or regression value for X.

        For a classification model, the predicted class for each sample in X is
        returned. For a regression model, the predicted value based on X is
        returned.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csr_matrix``.

        check_input : bool, default=True
            Allow to bypass several input checking.
            Don't use this parameter unless you know what you're doing.

        Returns
        -------
        y : array-like of shape (n_samples,) or (n_samples, n_outputs)
            The predicted classes, or the predict values.
        """
        check_is_fitted(self)
        X = self._validate_X_predict(X, check_input)
        proba = self.tree_.predict(X)
        n_samples = X.shape[0]

        # Classification
        if is_classifier(self):
            if self.n_outputs_ == 1:
                return self.classes_.take(np.argmax(proba, axis=1), axis=0)

            else:
                class_type = self.classes_[0].dtype
                predictions = np.zeros((n_samples, self.n_outputs_), dtype=class_type)
                for k in range(self.n_outputs_):
                    predictions[:, k] = self.classes_[k].take(
                        np.argmax(proba[:, k], axis=1), axis=0
                    )

                return predictions

        # Regression
        else:
            if self.n_outputs_ == 1:
                return proba[:, 0]

            else:
                return proba[:, :, 0]

    def apply(self, X, check_input=True):
        """Return the index of the leaf that each sample is predicted as.

        .. versionadded:: 0.17

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csr_matrix``.

        check_input : bool, default=True
            Allow to bypass several input checking.
            Don't use this parameter unless you know what you're doing.

        Returns
        -------
        X_leaves : array-like of shape (n_samples,)
            For each datapoint x in X, return the index of the leaf x
            ends up in. Leaves are numbered within
            ``[0; self.tree_.node_count)``, possibly with gaps in the
            numbering.
        """
        check_is_fitted(self)
        X = self._validate_X_predict(X, check_input)
        return self.tree_.apply(X)

    def decision_path(self, X, check_input=True):
        """Return the decision path in the tree.

        .. versionadded:: 0.18

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csr_matrix``.

        check_input : bool, default=True
            Allow to bypass several input checking.
            Don't use this parameter unless you know what you're doing.

        Returns
        -------
        indicator : sparse matrix of shape (n_samples, n_nodes)
            Return a node indicator CSR matrix where non zero elements
            indicates that the samples goes through the nodes.
        """
        X = self._validate_X_predict(X, check_input)
        return self.tree_.decision_path(X)

    def _prune_tree(self):
        """Prune tree using Minimal Cost-Complexity Pruning."""
        check_is_fitted(self)

        if self.ccp_alpha == 0.0:
            return

        # build pruned tree
        if is_classifier(self):
            n_classes = np.atleast_1d(self.n_classes_)
            pruned_tree = Tree(self.n_features_in_, n_classes, self.n_outputs_)
        else:
            pruned_tree = Tree(
                self.n_features_in_,
                # TODO: the tree shouldn't need this param
                np.array([1] * self.n_outputs_, dtype=np.intp),
                self.n_outputs_,
            )
        _build_pruned_tree_ccp(pruned_tree, self.tree_, self.ccp_alpha)

        self.tree_ = pruned_tree

    def cost_complexity_pruning_path(self, X, y, sample_weight=None):
        """Compute the pruning path during Minimal Cost-Complexity Pruning.

        See :ref:`minimal_cost_complexity_pruning` for details on the pruning
        process.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The training input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csc_matrix``.

        y : array-like of shape (n_samples,) or (n_samples, n_outputs)
            The target values (class labels) as integers or strings.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted. Splits
            that would create child nodes with net zero or negative weight are
            ignored while searching for a split in each node. Splits are also
            ignored if they would result in any single class carrying a
            negative weight in either child node.

        Returns
        -------
        ccp_path : :class:`~sklearn.utils.Bunch`
            Dictionary-like object, with the following attributes.

            ccp_alphas : ndarray
                Effective alphas of subtree during pruning.

            impurities : ndarray
                Sum of the impurities of the subtree leaves for the
                corresponding alpha value in ``ccp_alphas``.
        """
        est = clone(self).set_params(ccp_alpha=0.0)
        est.fit(X, y, sample_weight=sample_weight)
        return Bunch(**ccp_pruning_path(est.tree_))

    @property
    def feature_importances_(self):
        """Return the feature importances.

        The importance of a feature is computed as the (normalized) total
        reduction of the criterion brought by that feature.
        It is also known as the Gini importance.

        Warning: impurity-based feature importances can be misleading for
        high cardinality features (many unique values). See
        :func:`sklearn.inspection.permutation_importance` as an alternative.

        Returns
        -------
        feature_importances_ : ndarray of shape (n_features,)
            Normalized total reduction of criteria by feature
            (Gini importance).
        """
        check_is_fitted(self)

        return self.tree_.compute_feature_importances()

    def __sklearn_tags__(self):
        tags = super().__sklearn_tags__()
        tags.input_tags.sparse = True
        return tags


# =============================================================================
# Public estimators
# =============================================================================


class DecisionTreeClassifier(ClassifierMixin, BaseDecisionTree):
    """A decision tree classifier.

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

    Parameters
    ----------
    criterion : {"gini", "entropy", "log_loss"}, default="gini"
        The function to measure the quality of a split. Supported criteria are
        "gini" for the Gini impurity and "log_loss" and "entropy" both for the
        Shannon information gain, see :ref:`tree_mathematical_formulation`.

    splitter : {"best", "random"}, default="best"
        The strategy used to choose the split at each node. Supported
        strategies are "best" to choose the best split and "random" to choose
        the best random split.

    max_depth : int, default=None
        The maximum depth of the tree. If None, then nodes are expanded until
        all leaves are pure or until all leaves contain less than
        min_samples_split samples.

    min_samples_split : int or float, default=2
        The minimum number of samples required to split an internal node:

        - If int, then consider `min_samples_split` as the minimum number.
        - If float, then `min_samples_split` is a fraction and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_samples_leaf : int or float, default=1
        The minimum number of samples required to be at a leaf node.
        A split point at any depth will only be considered if it leaves at
        least ``min_samples_leaf`` training samples in each of the left and
        right branches.  This may have the effect of smoothing the model,
        especially in regression.

        - If int, then consider `min_samples_leaf` as the minimum number.
        - If float, then `min_samples_leaf` is a fraction and
          `ceil(min_samples_leaf * n_samples)` are the minimum
          number of samples for each node.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_weight_fraction_leaf : float, default=0.0
        The minimum weighted fraction of the sum total of weights (of all
        the input samples) required to be at a leaf node. Samples have
        equal weight when sample_weight is not provided.

    max_features : int, float or {"sqrt", "log2"}, default=None
        The number of features to consider when looking for the best split:

        - If int, then consider `max_features` features at each split.
        - If float, then `max_features` is a fraction and
          `max(1, int(max_features * n_features_in_))` features are considered at
          each split.
        - If "sqrt", then `max_features=sqrt(n_features)`.
        - If "log2", then `max_features=log2(n_features)`.
        - If None, then `max_features=n_features`.

        .. note::

            The search for a split does not stop until at least one
            valid partition of the node samples is found, even if it requires to
            effectively inspect more than ``max_features`` features.

    random_state : int, RandomState instance or None, default=None
        Controls the randomness of the estimator. The features are always
        randomly permuted at each split, even if ``splitter`` is set to
        ``"best"``. When ``max_features < n_features``, the algorithm will
        select ``max_features`` at random at each split before finding the best
        split among them. But the best found split may vary across different
        runs, even if ``max_features=n_features``. That is the case, if the
        improvement of the criterion is identical for several splits and one
        split has to be selected at random. To obtain a deterministic behaviour
        during fitting, ``random_state`` has to be fixed to an integer.
        See :term:`Glossary <random_state>` for details.

    max_leaf_nodes : int, default=None
        Grow a tree with ``max_leaf_nodes`` in best-first fashion.
        Best nodes are defined as relative reduction in impurity.
        If None then unlimited number of leaf nodes.

    min_impurity_decrease : float, default=0.0
        A node will be split if this split induces a decrease of the impurity
        greater than or equal to this value.

        The weighted impurity decrease equation is the following::

            N_t / N * (impurity - N_t_R / N_t * right_impurity
                                - N_t_L / N_t * left_impurity)

        where ``N`` is the total number of samples, ``N_t`` is the number of
        samples at the current node, ``N_t_L`` is the number of samples in the
        left child, and ``N_t_R`` is the number of samples in the right child.

        ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
        if ``sample_weight`` is passed.

        .. versionadded:: 0.19

    class_weight : dict, list of dict or "balanced", default=None
        Weights associated with classes in the form ``{class_label: weight}``.
        If None, all classes are supposed to have weight one. For
        multi-output problems, a list of dicts can be provided in the same
        order as the columns of y.

        Note that for multioutput (including multilabel) weights should be
        defined for each class of every column in its own dict. For example,
        for four-class multilabel classification weights should be
        [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
        [{1:1}, {2:5}, {3:1}, {4:1}].

        The "balanced" mode uses the values of y to automatically adjust
        weights inversely proportional to class frequencies in the input data
        as ``n_samples / (n_classes * np.bincount(y))``

        For multi-output, the weights of each column of y will be multiplied.

        Note that these weights will be multiplied with sample_weight (passed
        through the fit method) if sample_weight is specified.

    ccp_alpha : non-negative float, default=0.0
        Complexity parameter used for Minimal Cost-Complexity Pruning. The
        subtree with the largest cost complexity that is smaller than
        ``ccp_alpha`` will be chosen. By default, no pruning is performed. See
        :ref:`minimal_cost_complexity_pruning` for details. See
        :ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py`
        for an example of such pruning.

        .. versionadded:: 0.22

    monotonic_cst : array-like of int of shape (n_features), default=None
        Indicates the monotonicity constraint to enforce on each feature.
          - 1: monotonic increase
          - 0: no constraint
          - -1: monotonic decrease

        If monotonic_cst is None, no constraints are applied.

        Monotonicity constraints are not supported for:
          - multiclass classifications (i.e. when `n_classes > 2`),
          - multioutput classifications (i.e. when `n_outputs_ > 1`),
          - classifications trained on data with missing values.

        The constraints hold over the probability of the positive class.

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

        .. versionadded:: 1.4

    Attributes
    ----------
    classes_ : ndarray of shape (n_classes,) or list of ndarray
        The classes labels (single output problem),
        or a list of arrays of class labels (multi-output problem).

    feature_importances_ : ndarray of shape (n_features,)
        The impurity-based feature importances.
        The higher, the more important the feature.
        The importance of a feature is computed as the (normalized)
        total reduction of the criterion brought by that feature.  It is also
        known as the Gini importance [4]_.

        Warning: impurity-based feature importances can be misleading for
        high cardinality features (many unique values). See
        :func:`sklearn.inspection.permutation_importance` as an alternative.

    max_features_ : int
        The inferred value of max_features.

    n_classes_ : int or list of int
        The number of classes (for single output problems),
        or a list containing the number of classes for each
        output (for multi-output problems).

    n_features_in_ : int
        Number of features seen during :term:`fit`.

        .. versionadded:: 0.24

    feature_names_in_ : ndarray of shape (`n_features_in_`,)
        Names of features seen during :term:`fit`. Defined only when `X`
        has feature names that are all strings.

        .. versionadded:: 1.0

    n_outputs_ : int
        The number of outputs when ``fit`` is performed.

    tree_ : Tree instance
        The underlying Tree object. Please refer to
        ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and
        :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
        for basic usage of these attributes.

    See Also
    --------
    DecisionTreeRegressor : A decision tree regressor.

    Notes
    -----
    The default values for the parameters controlling the size of the trees
    (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
    unpruned trees which can potentially be very large on some data sets. To
    reduce memory consumption, the complexity and size of the trees should be
    controlled by setting those parameter values.

    The :meth:`predict` method operates using the :func:`numpy.argmax`
    function on the outputs of :meth:`predict_proba`. This means that in
    case the highest predicted probabilities are tied, the classifier will
    predict the tied class with the lowest index in :term:`classes_`.

    References
    ----------

    .. [1] https://en.wikipedia.org/wiki/Decision_tree_learning

    .. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
           and Regression Trees", Wadsworth, Belmont, CA, 1984.

    .. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
           Learning", Springer, 2009.

    .. [4] L. Breiman, and A. Cutler, "Random Forests",
           https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

    Examples
    --------
    >>> from sklearn.datasets import load_iris
    >>> from sklearn.model_selection import cross_val_score
    >>> from sklearn.tree import DecisionTreeClassifier
    >>> clf = DecisionTreeClassifier(random_state=0)
    >>> iris = load_iris()
    >>> cross_val_score(clf, iris.data, iris.target, cv=10)
    ...                             # doctest: +SKIP
    ...
    array([ 1.     ,  0.93...,  0.86...,  0.93...,  0.93...,
            0.93...,  0.93...,  1.     ,  0.93...,  1.      ])
    """

    # "check_input" is used for optimisation and isn't something to be passed
    # around in a pipeline.
    __metadata_request__predict_proba = {"check_input": metadata_routing.UNUSED}
    __metadata_request__fit = {"check_input": metadata_routing.UNUSED}

    _parameter_constraints: dict = {
        **BaseDecisionTree._parameter_constraints,
        "criterion": [StrOptions({"gini", "entropy", "log_loss"}), Hidden(Criterion)],
        "class_weight": [dict, list, StrOptions({"balanced"}), None],
    }

    def __init__(
        self,
        *,
        criterion="gini",
        splitter="best",
        max_depth=None,
        min_samples_split=2,
        min_samples_leaf=1,
        min_weight_fraction_leaf=0.0,
        max_features=None,
        random_state=None,
        max_leaf_nodes=None,
        min_impurity_decrease=0.0,
        class_weight=None,
        ccp_alpha=0.0,
        monotonic_cst=None,
    ):
        super().__init__(
            criterion=criterion,
            splitter=splitter,
            max_depth=max_depth,
            min_samples_split=min_samples_split,
            min_samples_leaf=min_samples_leaf,
            min_weight_fraction_leaf=min_weight_fraction_leaf,
            max_features=max_features,
            max_leaf_nodes=max_leaf_nodes,
            class_weight=class_weight,
            random_state=random_state,
            min_impurity_decrease=min_impurity_decrease,
            monotonic_cst=monotonic_cst,
            ccp_alpha=ccp_alpha,
        )

    @_fit_context(prefer_skip_nested_validation=True)
    def fit(self, X, y, sample_weight=None, check_input=True):
        """Build a decision tree classifier from the training set (X, y).

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The training input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csc_matrix``.

        y : array-like of shape (n_samples,) or (n_samples, n_outputs)
            The target values (class labels) as integers or strings.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted. Splits
            that would create child nodes with net zero or negative weight are
            ignored while searching for a split in each node. Splits are also
            ignored if they would result in any single class carrying a
            negative weight in either child node.

        check_input : bool, default=True
            Allow to bypass several input checking.
            Don't use this parameter unless you know what you're doing.

        Returns
        -------
        self : DecisionTreeClassifier
            Fitted estimator.
        """

        super()._fit(
            X,
            y,
            sample_weight=sample_weight,
            check_input=check_input,
        )
        return self

    def predict_proba(self, X, check_input=True):
        """Predict class probabilities of the input samples X.

        The predicted class probability is the fraction of samples of the same
        class in a leaf.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csr_matrix``.

        check_input : bool, default=True
            Allow to bypass several input checking.
            Don't use this parameter unless you know what you're doing.

        Returns
        -------
        proba : ndarray of shape (n_samples, n_classes) or 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_`.
        """
        check_is_fitted(self)
        X = self._validate_X_predict(X, check_input)
        proba = self.tree_.predict(X)

        if self.n_outputs_ == 1:
            return proba[:, : self.n_classes_]
        else:
            all_proba = []
            for k in range(self.n_outputs_):
                proba_k = proba[:, k, : self.n_classes_[k]]
                all_proba.append(proba_k)
            return all_proba

    def predict_log_proba(self, X):
        """Predict class log-probabilities of the input samples X.

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csr_matrix``.

        Returns
        -------
        proba : ndarray of shape (n_samples, n_classes) or list of n_outputs \
            such arrays if n_outputs > 1
            The class log-probabilities of the input samples. The order of the
            classes corresponds to that in the attribute :term:`classes_`.
        """
        proba = self.predict_proba(X)

        if self.n_outputs_ == 1:
            return np.log(proba)

        else:
            for k in range(self.n_outputs_):
                proba[k] = np.log(proba[k])

            return proba

    def __sklearn_tags__(self):
        tags = super().__sklearn_tags__()
        # XXX: nan is only support for dense arrays, but we set this for common test to
        # pass, specifically: check_estimators_nan_inf
        allow_nan = self.splitter in ("best", "random") and self.criterion in {
            "gini",
            "log_loss",
            "entropy",
        }
        tags.classifier_tags.multi_label = True
        tags.input_tags.allow_nan = allow_nan
        return tags


class DecisionTreeRegressor(RegressorMixin, BaseDecisionTree):
    """A decision tree regressor.

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

    Parameters
    ----------
    criterion : {"squared_error", "friedman_mse", "absolute_error", \
            "poisson"}, default="squared_error"
        The function to measure the quality of a split. Supported criteria
        are "squared_error" for the mean squared error, which is equal to
        variance reduction as feature selection criterion and minimizes the L2
        loss using the mean of each terminal node, "friedman_mse", which uses
        mean squared error with Friedman's improvement score for potential
        splits, "absolute_error" for the mean absolute error, which minimizes
        the L1 loss using the median of each terminal node, and "poisson" which
        uses reduction in the half mean Poisson deviance to find splits.

        .. versionadded:: 0.18
           Mean Absolute Error (MAE) criterion.

        .. versionadded:: 0.24
            Poisson deviance criterion.

    splitter : {"best", "random"}, default="best"
        The strategy used to choose the split at each node. Supported
        strategies are "best" to choose the best split and "random" to choose
        the best random split.

    max_depth : int, default=None
        The maximum depth of the tree. If None, then nodes are expanded until
        all leaves are pure or until all leaves contain less than
        min_samples_split samples.

        For an example of how ``max_depth`` influences the model, see
        :ref:`sphx_glr_auto_examples_tree_plot_tree_regression.py`.

    min_samples_split : int or float, default=2
        The minimum number of samples required to split an internal node:

        - If int, then consider `min_samples_split` as the minimum number.
        - If float, then `min_samples_split` is a fraction and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_samples_leaf : int or float, default=1
        The minimum number of samples required to be at a leaf node.
        A split point at any depth will only be considered if it leaves at
        least ``min_samples_leaf`` training samples in each of the left and
        right branches.  This may have the effect of smoothing the model,
        especially in regression.

        - If int, then consider `min_samples_leaf` as the minimum number.
        - If float, then `min_samples_leaf` is a fraction and
          `ceil(min_samples_leaf * n_samples)` are the minimum
          number of samples for each node.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_weight_fraction_leaf : float, default=0.0
        The minimum weighted fraction of the sum total of weights (of all
        the input samples) required to be at a leaf node. Samples have
        equal weight when sample_weight is not provided.

    max_features : int, float or {"sqrt", "log2"}, default=None
        The number of features to consider when looking for the best split:

        - If int, then consider `max_features` features at each split.
        - If float, then `max_features` is a fraction and
          `max(1, int(max_features * n_features_in_))` features are considered at each
          split.
        - If "sqrt", then `max_features=sqrt(n_features)`.
        - If "log2", then `max_features=log2(n_features)`.
        - If None, then `max_features=n_features`.

        Note: the search for a split does not stop until at least one
        valid partition of the node samples is found, even if it requires to
        effectively inspect more than ``max_features`` features.

    random_state : int, RandomState instance or None, default=None
        Controls the randomness of the estimator. The features are always
        randomly permuted at each split, even if ``splitter`` is set to
        ``"best"``. When ``max_features < n_features``, the algorithm will
        select ``max_features`` at random at each split before finding the best
        split among them. But the best found split may vary across different
        runs, even if ``max_features=n_features``. That is the case, if the
        improvement of the criterion is identical for several splits and one
        split has to be selected at random. To obtain a deterministic behaviour
        during fitting, ``random_state`` has to be fixed to an integer.
        See :term:`Glossary <random_state>` for details.

    max_leaf_nodes : int, default=None
        Grow a tree with ``max_leaf_nodes`` in best-first fashion.
        Best nodes are defined as relative reduction in impurity.
        If None then unlimited number of leaf nodes.

    min_impurity_decrease : float, default=0.0
        A node will be split if this split induces a decrease of the impurity
        greater than or equal to this value.

        The weighted impurity decrease equation is the following::

            N_t / N * (impurity - N_t_R / N_t * right_impurity
                                - N_t_L / N_t * left_impurity)

        where ``N`` is the total number of samples, ``N_t`` is the number of
        samples at the current node, ``N_t_L`` is the number of samples in the
        left child, and ``N_t_R`` is the number of samples in the right child.

        ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
        if ``sample_weight`` is passed.

        .. versionadded:: 0.19

    ccp_alpha : non-negative float, default=0.0
        Complexity parameter used for Minimal Cost-Complexity Pruning. The
        subtree with the largest cost complexity that is smaller than
        ``ccp_alpha`` will be chosen. By default, no pruning is performed. See
        :ref:`minimal_cost_complexity_pruning` for details. See
        :ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py`
        for an example of such pruning.

        .. versionadded:: 0.22

    monotonic_cst : array-like of int of shape (n_features), default=None
        Indicates the monotonicity constraint to enforce on each feature.
          - 1: monotonic increase
          - 0: no constraint
          - -1: monotonic decrease

        If monotonic_cst is None, no constraints are applied.

        Monotonicity constraints are not supported for:
          - multioutput regressions (i.e. when `n_outputs_ > 1`),
          - regressions trained on data with missing values.

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

        .. versionadded:: 1.4

    Attributes
    ----------
    feature_importances_ : ndarray of shape (n_features,)
        The feature importances.
        The higher, the more important the feature.
        The importance of a feature is computed as the
        (normalized) total reduction of the criterion brought
        by that feature. It is also known as the Gini importance [4]_.

        Warning: impurity-based feature importances can be misleading for
        high cardinality features (many unique values). See
        :func:`sklearn.inspection.permutation_importance` as an alternative.

    max_features_ : int
        The inferred value of max_features.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

        .. versionadded:: 0.24

    feature_names_in_ : ndarray of shape (`n_features_in_`,)
        Names of features seen during :term:`fit`. Defined only when `X`
        has feature names that are all strings.

        .. versionadded:: 1.0

    n_outputs_ : int
        The number of outputs when ``fit`` is performed.

    tree_ : Tree instance
        The underlying Tree object. Please refer to
        ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and
        :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
        for basic usage of these attributes.

    See Also
    --------
    DecisionTreeClassifier : A decision tree classifier.

    Notes
    -----
    The default values for the parameters controlling the size of the trees
    (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
    unpruned trees which can potentially be very large on some data sets. To
    reduce memory consumption, the complexity and size of the trees should be
    controlled by setting those parameter values.

    References
    ----------

    .. [1] https://en.wikipedia.org/wiki/Decision_tree_learning

    .. [2] L. Breiman, J. Friedman, R. Olshen, and C. Stone, "Classification
           and Regression Trees", Wadsworth, Belmont, CA, 1984.

    .. [3] T. Hastie, R. Tibshirani and J. Friedman. "Elements of Statistical
           Learning", Springer, 2009.

    .. [4] L. Breiman, and A. Cutler, "Random Forests",
           https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

    Examples
    --------
    >>> from sklearn.datasets import load_diabetes
    >>> from sklearn.model_selection import cross_val_score
    >>> from sklearn.tree import DecisionTreeRegressor
    >>> X, y = load_diabetes(return_X_y=True)
    >>> regressor = DecisionTreeRegressor(random_state=0)
    >>> cross_val_score(regressor, X, y, cv=10)
    ...                    # doctest: +SKIP
    ...
    array([-0.39..., -0.46...,  0.02...,  0.06..., -0.50...,
           0.16...,  0.11..., -0.73..., -0.30..., -0.00...])
    """

    # "check_input" is used for optimisation and isn't something to be passed
    # around in a pipeline.
    __metadata_request__fit = {"check_input": metadata_routing.UNUSED}

    _parameter_constraints: dict = {
        **BaseDecisionTree._parameter_constraints,
        "criterion": [
            StrOptions({"squared_error", "friedman_mse", "absolute_error", "poisson"}),
            Hidden(Criterion),
        ],
    }

    def __init__(
        self,
        *,
        criterion="squared_error",
        splitter="best",
        max_depth=None,
        min_samples_split=2,
        min_samples_leaf=1,
        min_weight_fraction_leaf=0.0,
        max_features=None,
        random_state=None,
        max_leaf_nodes=None,
        min_impurity_decrease=0.0,
        ccp_alpha=0.0,
        monotonic_cst=None,
    ):
        super().__init__(
            criterion=criterion,
            splitter=splitter,
            max_depth=max_depth,
            min_samples_split=min_samples_split,
            min_samples_leaf=min_samples_leaf,
            min_weight_fraction_leaf=min_weight_fraction_leaf,
            max_features=max_features,
            max_leaf_nodes=max_leaf_nodes,
            random_state=random_state,
            min_impurity_decrease=min_impurity_decrease,
            ccp_alpha=ccp_alpha,
            monotonic_cst=monotonic_cst,
        )

    @_fit_context(prefer_skip_nested_validation=True)
    def fit(self, X, y, sample_weight=None, check_input=True):
        """Build a decision tree regressor from the training set (X, y).

        Parameters
        ----------
        X : {array-like, sparse matrix} of shape (n_samples, n_features)
            The training input samples. Internally, it will be converted to
            ``dtype=np.float32`` and if a sparse matrix is provided
            to a sparse ``csc_matrix``.

        y : array-like of shape (n_samples,) or (n_samples, n_outputs)
            The target values (real numbers). Use ``dtype=np.float64`` and
            ``order='C'`` for maximum efficiency.

        sample_weight : array-like of shape (n_samples,), default=None
            Sample weights. If None, then samples are equally weighted. Splits
            that would create child nodes with net zero or negative weight are
            ignored while searching for a split in each node.

        check_input : bool, default=True
            Allow to bypass several input checking.
            Don't use this parameter unless you know what you're doing.

        Returns
        -------
        self : DecisionTreeRegressor
            Fitted estimator.
        """

        super()._fit(
            X,
            y,
            sample_weight=sample_weight,
            check_input=check_input,
        )
        return self

    def _compute_partial_dependence_recursion(self, grid, target_features):
        """Fast partial dependence computation.

        Parameters
        ----------
        grid : ndarray of shape (n_samples, n_target_features), dtype=np.float32
            The grid points on which the partial dependence should be
            evaluated.
        target_features : ndarray of shape (n_target_features), dtype=np.intp
            The set of target features for which the partial dependence
            should be evaluated.

        Returns
        -------
        averaged_predictions : ndarray of shape (n_samples,), dtype=np.float64
            The value of the partial dependence function on each grid point.
        """
        grid = np.asarray(grid, dtype=DTYPE, order="C")
        averaged_predictions = np.zeros(
            shape=grid.shape[0], dtype=np.float64, order="C"
        )
        target_features = np.asarray(target_features, dtype=np.intp, order="C")

        self.tree_.compute_partial_dependence(
            grid, target_features, averaged_predictions
        )
        return averaged_predictions

    def __sklearn_tags__(self):
        tags = super().__sklearn_tags__()
        # XXX: nan is only support for dense arrays, but we set this for common test to
        # pass, specifically: check_estimators_nan_inf
        allow_nan = self.splitter in ("best", "random") and self.criterion in {
            "squared_error",
            "friedman_mse",
            "poisson",
        }
        tags.input_tags.allow_nan = allow_nan
        return tags


class ExtraTreeClassifier(DecisionTreeClassifier):
    """An extremely randomized tree classifier.

    Extra-trees differ from classic decision trees in the way they are built.
    When looking for the best split to separate the samples of a node into two
    groups, random splits are drawn for each of the `max_features` randomly
    selected features and the best split among those is chosen. When
    `max_features` is set 1, this amounts to building a totally random
    decision tree.

    Warning: Extra-trees should only be used within ensemble methods.

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

    Parameters
    ----------
    criterion : {"gini", "entropy", "log_loss"}, default="gini"
        The function to measure the quality of a split. Supported criteria are
        "gini" for the Gini impurity and "log_loss" and "entropy" both for the
        Shannon information gain, see :ref:`tree_mathematical_formulation`.

    splitter : {"random", "best"}, default="random"
        The strategy used to choose the split at each node. Supported
        strategies are "best" to choose the best split and "random" to choose
        the best random split.

    max_depth : int, default=None
        The maximum depth of the tree. If None, then nodes are expanded until
        all leaves are pure or until all leaves contain less than
        min_samples_split samples.

    min_samples_split : int or float, default=2
        The minimum number of samples required to split an internal node:

        - If int, then consider `min_samples_split` as the minimum number.
        - If float, then `min_samples_split` is a fraction and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_samples_leaf : int or float, default=1
        The minimum number of samples required to be at a leaf node.
        A split point at any depth will only be considered if it leaves at
        least ``min_samples_leaf`` training samples in each of the left and
        right branches.  This may have the effect of smoothing the model,
        especially in regression.

        - If int, then consider `min_samples_leaf` as the minimum number.
        - If float, then `min_samples_leaf` is a fraction and
          `ceil(min_samples_leaf * n_samples)` are the minimum
          number of samples for each node.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_weight_fraction_leaf : float, default=0.0
        The minimum weighted fraction of the sum total of weights (of all
        the input samples) required to be at a leaf node. Samples have
        equal weight when sample_weight is not provided.

    max_features : int, float, {"sqrt", "log2"} or None, default="sqrt"
        The number of features to consider when looking for the best split:

        - If int, then consider `max_features` features at each split.
        - If float, then `max_features` is a fraction and
          `max(1, int(max_features * n_features_in_))` features are considered at
          each split.
        - If "sqrt", then `max_features=sqrt(n_features)`.
        - If "log2", then `max_features=log2(n_features)`.
        - If None, then `max_features=n_features`.

        .. versionchanged:: 1.1
            The default of `max_features` changed from `"auto"` to `"sqrt"`.

        Note: the search for a split does not stop until at least one
        valid partition of the node samples is found, even if it requires to
        effectively inspect more than ``max_features`` features.

    random_state : int, RandomState instance or None, default=None
        Used to pick randomly the `max_features` used at each split.
        See :term:`Glossary <random_state>` for details.

    max_leaf_nodes : int, default=None
        Grow a tree with ``max_leaf_nodes`` in best-first fashion.
        Best nodes are defined as relative reduction in impurity.
        If None then unlimited number of leaf nodes.

    min_impurity_decrease : float, default=0.0
        A node will be split if this split induces a decrease of the impurity
        greater than or equal to this value.

        The weighted impurity decrease equation is the following::

            N_t / N * (impurity - N_t_R / N_t * right_impurity
                                - N_t_L / N_t * left_impurity)

        where ``N`` is the total number of samples, ``N_t`` is the number of
        samples at the current node, ``N_t_L`` is the number of samples in the
        left child, and ``N_t_R`` is the number of samples in the right child.

        ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
        if ``sample_weight`` is passed.

        .. versionadded:: 0.19

    class_weight : dict, list of dict or "balanced", default=None
        Weights associated with classes in the form ``{class_label: weight}``.
        If None, all classes are supposed to have weight one. For
        multi-output problems, a list of dicts can be provided in the same
        order as the columns of y.

        Note that for multioutput (including multilabel) weights should be
        defined for each class of every column in its own dict. For example,
        for four-class multilabel classification weights should be
        [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of
        [{1:1}, {2:5}, {3:1}, {4:1}].

        The "balanced" mode uses the values of y to automatically adjust
        weights inversely proportional to class frequencies in the input data
        as ``n_samples / (n_classes * np.bincount(y))``

        For multi-output, the weights of each column of y will be multiplied.

        Note that these weights will be multiplied with sample_weight (passed
        through the fit method) if sample_weight is specified.

    ccp_alpha : non-negative float, default=0.0
        Complexity parameter used for Minimal Cost-Complexity Pruning. The
        subtree with the largest cost complexity that is smaller than
        ``ccp_alpha`` will be chosen. By default, no pruning is performed. See
        :ref:`minimal_cost_complexity_pruning` for details. See
        :ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py`
        for an example of such pruning.

        .. versionadded:: 0.22

    monotonic_cst : array-like of int of shape (n_features), default=None
        Indicates the monotonicity constraint to enforce on each feature.
          - 1: monotonic increase
          - 0: no constraint
          - -1: monotonic decrease

        If monotonic_cst is None, no constraints are applied.

        Monotonicity constraints are not supported for:
          - multiclass classifications (i.e. when `n_classes > 2`),
          - multioutput classifications (i.e. when `n_outputs_ > 1`),
          - classifications trained on data with missing values.

        The constraints hold over the probability of the positive class.

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

        .. versionadded:: 1.4

    Attributes
    ----------
    classes_ : ndarray of shape (n_classes,) or list of ndarray
        The classes labels (single output problem),
        or a list of arrays of class labels (multi-output problem).

    max_features_ : int
        The inferred value of max_features.

    n_classes_ : int or list of int
        The number of classes (for single output problems),
        or a list containing the number of classes for each
        output (for multi-output problems).

    feature_importances_ : ndarray of shape (n_features,)
        The impurity-based feature importances.
        The higher, the more important the feature.
        The importance of a feature is computed as the (normalized)
        total reduction of the criterion brought by that feature.  It is also
        known as the Gini importance.

        Warning: impurity-based feature importances can be misleading for
        high cardinality features (many unique values). See
        :func:`sklearn.inspection.permutation_importance` as an alternative.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

        .. versionadded:: 0.24

    feature_names_in_ : ndarray of shape (`n_features_in_`,)
        Names of features seen during :term:`fit`. Defined only when `X`
        has feature names that are all strings.

        .. versionadded:: 1.0

    n_outputs_ : int
        The number of outputs when ``fit`` is performed.

    tree_ : Tree instance
        The underlying Tree object. Please refer to
        ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and
        :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
        for basic usage of these attributes.

    See Also
    --------
    ExtraTreeRegressor : An extremely randomized tree regressor.
    sklearn.ensemble.ExtraTreesClassifier : An extra-trees classifier.
    sklearn.ensemble.ExtraTreesRegressor : An extra-trees regressor.
    sklearn.ensemble.RandomForestClassifier : A random forest classifier.
    sklearn.ensemble.RandomForestRegressor : A random forest regressor.
    sklearn.ensemble.RandomTreesEmbedding : An ensemble of
        totally random trees.

    Notes
    -----
    The default values for the parameters controlling the size of the trees
    (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
    unpruned trees which can potentially be very large on some data sets. To
    reduce memory consumption, the complexity and size of the trees should be
    controlled by setting those parameter values.

    References
    ----------

    .. [1] P. Geurts, D. Ernst., and L. Wehenkel, "Extremely randomized trees",
           Machine Learning, 63(1), 3-42, 2006.

    Examples
    --------
    >>> from sklearn.datasets import load_iris
    >>> from sklearn.model_selection import train_test_split
    >>> from sklearn.ensemble import BaggingClassifier
    >>> from sklearn.tree import ExtraTreeClassifier
    >>> X, y = load_iris(return_X_y=True)
    >>> X_train, X_test, y_train, y_test = train_test_split(
    ...    X, y, random_state=0)
    >>> extra_tree = ExtraTreeClassifier(random_state=0)
    >>> cls = BaggingClassifier(extra_tree, random_state=0).fit(
    ...    X_train, y_train)
    >>> cls.score(X_test, y_test)
    0.8947...
    """

    def __init__(
        self,
        *,
        criterion="gini",
        splitter="random",
        max_depth=None,
        min_samples_split=2,
        min_samples_leaf=1,
        min_weight_fraction_leaf=0.0,
        max_features="sqrt",
        random_state=None,
        max_leaf_nodes=None,
        min_impurity_decrease=0.0,
        class_weight=None,
        ccp_alpha=0.0,
        monotonic_cst=None,
    ):
        super().__init__(
            criterion=criterion,
            splitter=splitter,
            max_depth=max_depth,
            min_samples_split=min_samples_split,
            min_samples_leaf=min_samples_leaf,
            min_weight_fraction_leaf=min_weight_fraction_leaf,
            max_features=max_features,
            max_leaf_nodes=max_leaf_nodes,
            class_weight=class_weight,
            min_impurity_decrease=min_impurity_decrease,
            random_state=random_state,
            ccp_alpha=ccp_alpha,
            monotonic_cst=monotonic_cst,
        )

    def __sklearn_tags__(self):
        tags = super().__sklearn_tags__()
        # XXX: nan is only supported for dense arrays, but we set this for the
        # common test to pass, specifically: check_estimators_nan_inf
        allow_nan = self.splitter == "random" and self.criterion in {
            "gini",
            "log_loss",
            "entropy",
        }
        tags.classifier_tags.multi_label = True
        tags.input_tags.allow_nan = allow_nan
        return tags


class ExtraTreeRegressor(DecisionTreeRegressor):
    """An extremely randomized tree regressor.

    Extra-trees differ from classic decision trees in the way they are built.
    When looking for the best split to separate the samples of a node into two
    groups, random splits are drawn for each of the `max_features` randomly
    selected features and the best split among those is chosen. When
    `max_features` is set 1, this amounts to building a totally random
    decision tree.

    Warning: Extra-trees should only be used within ensemble methods.

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

    Parameters
    ----------
    criterion : {"squared_error", "friedman_mse", "absolute_error", "poisson"}, \
            default="squared_error"
        The function to measure the quality of a split. Supported criteria
        are "squared_error" for the mean squared error, which is equal to
        variance reduction as feature selection criterion and minimizes the L2
        loss using the mean of each terminal node, "friedman_mse", which uses
        mean squared error with Friedman's improvement score for potential
        splits, "absolute_error" for the mean absolute error, which minimizes
        the L1 loss using the median of each terminal node, and "poisson" which
        uses reduction in Poisson deviance to find splits.

        .. versionadded:: 0.18
           Mean Absolute Error (MAE) criterion.

        .. versionadded:: 0.24
            Poisson deviance criterion.

    splitter : {"random", "best"}, default="random"
        The strategy used to choose the split at each node. Supported
        strategies are "best" to choose the best split and "random" to choose
        the best random split.

    max_depth : int, default=None
        The maximum depth of the tree. If None, then nodes are expanded until
        all leaves are pure or until all leaves contain less than
        min_samples_split samples.

    min_samples_split : int or float, default=2
        The minimum number of samples required to split an internal node:

        - If int, then consider `min_samples_split` as the minimum number.
        - If float, then `min_samples_split` is a fraction and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_samples_leaf : int or float, default=1
        The minimum number of samples required to be at a leaf node.
        A split point at any depth will only be considered if it leaves at
        least ``min_samples_leaf`` training samples in each of the left and
        right branches.  This may have the effect of smoothing the model,
        especially in regression.

        - If int, then consider `min_samples_leaf` as the minimum number.
        - If float, then `min_samples_leaf` is a fraction and
          `ceil(min_samples_leaf * n_samples)` are the minimum
          number of samples for each node.

        .. versionchanged:: 0.18
           Added float values for fractions.

    min_weight_fraction_leaf : float, default=0.0
        The minimum weighted fraction of the sum total of weights (of all
        the input samples) required to be at a leaf node. Samples have
        equal weight when sample_weight is not provided.

    max_features : int, float, {"sqrt", "log2"} or None, default=1.0
        The number of features to consider when looking for the best split:

        - If int, then consider `max_features` features at each split.
        - If float, then `max_features` is a fraction and
          `max(1, int(max_features * n_features_in_))` features are considered at each
          split.
        - If "sqrt", then `max_features=sqrt(n_features)`.
        - If "log2", then `max_features=log2(n_features)`.
        - If None, then `max_features=n_features`.

        .. versionchanged:: 1.1
            The default of `max_features` changed from `"auto"` to `1.0`.

        Note: the search for a split does not stop until at least one
        valid partition of the node samples is found, even if it requires to
        effectively inspect more than ``max_features`` features.

    random_state : int, RandomState instance or None, default=None
        Used to pick randomly the `max_features` used at each split.
        See :term:`Glossary <random_state>` for details.

    min_impurity_decrease : float, default=0.0
        A node will be split if this split induces a decrease of the impurity
        greater than or equal to this value.

        The weighted impurity decrease equation is the following::

            N_t / N * (impurity - N_t_R / N_t * right_impurity
                                - N_t_L / N_t * left_impurity)

        where ``N`` is the total number of samples, ``N_t`` is the number of
        samples at the current node, ``N_t_L`` is the number of samples in the
        left child, and ``N_t_R`` is the number of samples in the right child.

        ``N``, ``N_t``, ``N_t_R`` and ``N_t_L`` all refer to the weighted sum,
        if ``sample_weight`` is passed.

        .. versionadded:: 0.19

    max_leaf_nodes : int, default=None
        Grow a tree with ``max_leaf_nodes`` in best-first fashion.
        Best nodes are defined as relative reduction in impurity.
        If None then unlimited number of leaf nodes.

    ccp_alpha : non-negative float, default=0.0
        Complexity parameter used for Minimal Cost-Complexity Pruning. The
        subtree with the largest cost complexity that is smaller than
        ``ccp_alpha`` will be chosen. By default, no pruning is performed. See
        :ref:`minimal_cost_complexity_pruning` for details. See
        :ref:`sphx_glr_auto_examples_tree_plot_cost_complexity_pruning.py`
        for an example of such pruning.

        .. versionadded:: 0.22

    monotonic_cst : array-like of int of shape (n_features), default=None
        Indicates the monotonicity constraint to enforce on each feature.
          - 1: monotonic increase
          - 0: no constraint
          - -1: monotonic decrease

        If monotonic_cst is None, no constraints are applied.

        Monotonicity constraints are not supported for:
          - multioutput regressions (i.e. when `n_outputs_ > 1`),
          - regressions trained on data with missing values.

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

        .. versionadded:: 1.4

    Attributes
    ----------
    max_features_ : int
        The inferred value of max_features.

    n_features_in_ : int
        Number of features seen during :term:`fit`.

        .. versionadded:: 0.24

    feature_names_in_ : ndarray of shape (`n_features_in_`,)
        Names of features seen during :term:`fit`. Defined only when `X`
        has feature names that are all strings.

        .. versionadded:: 1.0

    feature_importances_ : ndarray of shape (n_features,)
        Return impurity-based feature importances (the higher, the more
        important the feature).

        Warning: impurity-based feature importances can be misleading for
        high cardinality features (many unique values). See
        :func:`sklearn.inspection.permutation_importance` as an alternative.

    n_outputs_ : int
        The number of outputs when ``fit`` is performed.

    tree_ : Tree instance
        The underlying Tree object. Please refer to
        ``help(sklearn.tree._tree.Tree)`` for attributes of Tree object and
        :ref:`sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py`
        for basic usage of these attributes.

    See Also
    --------
    ExtraTreeClassifier : An extremely randomized tree classifier.
    sklearn.ensemble.ExtraTreesClassifier : An extra-trees classifier.
    sklearn.ensemble.ExtraTreesRegressor : An extra-trees regressor.

    Notes
    -----
    The default values for the parameters controlling the size of the trees
    (e.g. ``max_depth``, ``min_samples_leaf``, etc.) lead to fully grown and
    unpruned trees which can potentially be very large on some data sets. To
    reduce memory consumption, the complexity and size of the trees should be
    controlled by setting those parameter values.

    References
    ----------

    .. [1] P. Geurts, D. Ernst., and L. Wehenkel, "Extremely randomized trees",
           Machine Learning, 63(1), 3-42, 2006.

    Examples
    --------
    >>> from sklearn.datasets import load_diabetes
    >>> from sklearn.model_selection import train_test_split
    >>> from sklearn.ensemble import BaggingRegressor
    >>> from sklearn.tree import ExtraTreeRegressor
    >>> X, y = load_diabetes(return_X_y=True)
    >>> X_train, X_test, y_train, y_test = train_test_split(
    ...     X, y, random_state=0)
    >>> extra_tree = ExtraTreeRegressor(random_state=0)
    >>> reg = BaggingRegressor(extra_tree, random_state=0).fit(
    ...     X_train, y_train)
    >>> reg.score(X_test, y_test)
    0.33...
    """

    def __init__(
        self,
        *,
        criterion="squared_error",
        splitter="random",
        max_depth=None,
        min_samples_split=2,
        min_samples_leaf=1,
        min_weight_fraction_leaf=0.0,
        max_features=1.0,
        random_state=None,
        min_impurity_decrease=0.0,
        max_leaf_nodes=None,
        ccp_alpha=0.0,
        monotonic_cst=None,
    ):
        super().__init__(
            criterion=criterion,
            splitter=splitter,
            max_depth=max_depth,
            min_samples_split=min_samples_split,
            min_samples_leaf=min_samples_leaf,
            min_weight_fraction_leaf=min_weight_fraction_leaf,
            max_features=max_features,
            max_leaf_nodes=max_leaf_nodes,
            min_impurity_decrease=min_impurity_decrease,
            random_state=random_state,
            ccp_alpha=ccp_alpha,
            monotonic_cst=monotonic_cst,
        )

    def __sklearn_tags__(self):
        tags = super().__sklearn_tags__()
        # XXX: nan is only supported for dense arrays, but we set this for the
        # common test to pass, specifically: check_estimators_nan_inf
        allow_nan = self.splitter == "random" and self.criterion in {
            "squared_error",
            "friedman_mse",
            "poisson",
        }
        tags.input_tags.allow_nan = allow_nan
        return tags