forest.py

"""Forest of trees-based ensemble methods

Those methods include random forests and extremely randomized trees.

The module structure is the following:

- The ``BaseForest`` base class implements a common ``fit`` method for all
  the estimators in the module. The ``fit`` method of the base ``Forest``
  class calls the ``fit`` method of each sub-estimator on random samples
  (with replacement, a.k.a. bootstrap) of the training set.

  The init of the sub-estimator is further delegated to the
  ``BaseEnsemble`` constructor.

- The ``ForestClassifier`` and ``ForestRegressor`` base classes further
  implement the prediction logic by computing an average of the predicted
  outcomes of the sub-estimators.

- The ``RandomForestClassifier`` and ``RandomForestRegressor`` derived
  classes provide the user with concrete implementations of
  the forest ensemble method using classical, deterministic
  ``DecisionTreeClassifier`` and ``DecisionTreeRegressor`` as
  sub-estimator implementations.

- The ``ExtraTreesClassifier`` and ``ExtraTreesRegressor`` derived
  classes provide the user with concrete implementations of the
  forest ensemble method using the extremely randomized trees
  ``ExtraTreeClassifier`` and ``ExtraTreeRegressor`` as
  sub-estimator implementations.

Single and multi-output problems are both handled.

"""

# Authors: Gilles Louppe <g.louppe@gmail.com>
#          Brian Holt <bdholt1@gmail.com>
#          Joly Arnaud <arnaud.v.joly@gmail.com>
#          Fares Hedayati <fares.hedayati@gmail.com>
#
# License: BSD 3 clause

from __future__ import division

import warnings
from warnings import warn

from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.sparse import issparse
from scipy.sparse import hstack as sparse_hstack


from ..base import ClassifierMixin, RegressorMixin
from ..externals.joblib import Parallel, delayed
from ..externals import six
from ..metrics import r2_score
from ..preprocessing import OneHotEncoder
from ..tree import (DecisionTreeClassifier, DecisionTreeRegressor,
                    ExtraTreeClassifier, ExtraTreeRegressor)
from ..tree._tree import DTYPE, DOUBLE
from ..utils import check_random_state, check_array, compute_sample_weight
from ..exceptions import DataConversionWarning, NotFittedError
from .base import BaseEnsemble, _partition_estimators
from ..utils.fixes import bincount, parallel_helper
from ..utils.multiclass import check_classification_targets
from ..utils.validation import check_is_fitted

__all__ = ["RandomForestClassifier",
           "RandomForestRegressor",
           "ExtraTreesClassifier",
           "ExtraTreesRegressor",
           "RandomTreesEmbedding"]

MAX_INT = np.iinfo(np.int32).max


def _generate_sample_indices(random_state, n_samples):
    """Private function used to _parallel_build_trees function."""
    random_instance = check_random_state(random_state)
    sample_indices = random_instance.randint(0, n_samples, n_samples)

    return sample_indices


def _generate_unsampled_indices(random_state, n_samples):
    """Private function used to forest._set_oob_score function."""
    sample_indices = _generate_sample_indices(random_state, n_samples)
    sample_counts = bincount(sample_indices, minlength=n_samples)
    unsampled_mask = sample_counts == 0
    indices_range = np.arange(n_samples)
    unsampled_indices = indices_range[unsampled_mask]

    return unsampled_indices


def _parallel_build_trees(tree, forest, X, y, sample_weight, tree_idx, n_trees,
                          verbose=0, class_weight=None):
    """Private function used to fit a single tree in parallel."""
    if verbose > 1:
        print("building tree %d of %d" % (tree_idx + 1, n_trees))

    if forest.bootstrap:
        n_samples = X.shape[0]
        if sample_weight is None:
            curr_sample_weight = np.ones((n_samples,), dtype=np.float64)
        else:
            curr_sample_weight = sample_weight.copy()

        indices = _generate_sample_indices(tree.random_state, n_samples)
        sample_counts = bincount(indices, minlength=n_samples)
        curr_sample_weight *= sample_counts

        if class_weight == 'subsample':
            with warnings.catch_warnings():
                warnings.simplefilter('ignore', DeprecationWarning)
                curr_sample_weight *= compute_sample_weight('auto', y, indices)
        elif class_weight == 'balanced_subsample':
            curr_sample_weight *= compute_sample_weight('balanced', y, indices)

        tree.fit(X, y, sample_weight=curr_sample_weight, check_input=False)
    else:
        tree.fit(X, y, sample_weight=sample_weight, check_input=False)

    return tree


class BaseForest(six.with_metaclass(ABCMeta, BaseEnsemble)):
    """Base class for forests of trees.

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

    @abstractmethod
    def __init__(self,
                 base_estimator,
                 n_estimators=10,
                 estimator_params=tuple(),
                 bootstrap=False,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False,
                 class_weight=None):
        super(BaseForest, self).__init__(
            base_estimator=base_estimator,
            n_estimators=n_estimators,
            estimator_params=estimator_params)

        self.bootstrap = bootstrap
        self.oob_score = oob_score
        self.n_jobs = n_jobs
        self.random_state = random_state
        self.verbose = verbose
        self.warm_start = warm_start
        self.class_weight = class_weight

    def apply(self, X):
        """Apply trees in the forest to X, return leaf indices.

        Parameters
        ----------
        X : array-like or sparse matrix, shape = [n_samples, n_features]
            The input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csr_matrix``.

        Returns
        -------
        X_leaves : array_like, shape = [n_samples, n_estimators]
            For each datapoint x in X and for each tree in the forest,
            return the index of the leaf x ends up in.
        """
        X = self._validate_X_predict(X)
        results = Parallel(n_jobs=self.n_jobs, verbose=self.verbose,
                           backend="threading")(
            delayed(parallel_helper)(tree, 'apply', X, check_input=False)
            for tree in self.estimators_)

        return np.array(results).T

    def decision_path(self, X):
        """Return the decision path in the forest

        .. versionadded:: 0.18

        Parameters
        ----------
        X : array-like or sparse matrix, shape = [n_samples, n_features]
            The input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csr_matrix``.

        Returns
        -------
        indicator : sparse csr array, shape = [n_samples, n_nodes]
            Return a node indicator matrix where non zero elements
            indicates that the samples goes through the nodes.

        n_nodes_ptr : array of size (n_estimators + 1, )
            The columns from indicator[n_nodes_ptr[i]:n_nodes_ptr[i+1]]
            gives the indicator value for the i-th estimator.

        """
        X = self._validate_X_predict(X)
        indicators = Parallel(n_jobs=self.n_jobs, verbose=self.verbose,
                              backend="threading")(
            delayed(parallel_helper)(tree, 'decision_path', X,
                                      check_input=False)
            for tree in self.estimators_)

        n_nodes = [0]
        n_nodes.extend([i.shape[1] for i in indicators])
        n_nodes_ptr = np.array(n_nodes).cumsum()

        return sparse_hstack(indicators).tocsr(), n_nodes_ptr

    def fit(self, X, y, sample_weight=None):
        """Build a forest of trees from the training set (X, y).

        Parameters
        ----------
        X : array-like or sparse matrix of shape = [n_samples, n_features]
            The training input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csc_matrix``.

        y : array-like, shape = [n_samples] or [n_samples, n_outputs]
            The target values (class labels in classification, real numbers in
            regression).

        sample_weight : array-like, shape = [n_samples] or 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. In the case of
            classification, splits are also ignored if they would result in any
            single class carrying a negative weight in either child node.

        Returns
        -------
        self : object
            Returns self.
        """
        # Validate or convert input data
        X = check_array(X, accept_sparse="csc", dtype=DTYPE)
        y = check_array(y, accept_sparse='csc', ensure_2d=False, dtype=None)
        if sample_weight is not None:
            sample_weight = check_array(sample_weight, ensure_2d=False)
        if issparse(X):
            # Pre-sort indices to avoid that each individual tree of the
            # ensemble sorts the indices.
            X.sort_indices()

        # Remap output
        n_samples, self.n_features_ = X.shape

        y = np.atleast_1d(y)
        if y.ndim == 2 and y.shape[1] == 1:
            warn("A column-vector y was passed when a 1d array was"
                 " expected. Please change the shape of y to "
                 "(n_samples,), for example using ravel().",
                 DataConversionWarning, stacklevel=2)

        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]

        y, expanded_class_weight = self._validate_y_class_weight(y)

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

        # Check parameters
        self._validate_estimator()

        if not self.bootstrap and self.oob_score:
            raise ValueError("Out of bag estimation only available"
                             " if bootstrap=True")

        random_state = check_random_state(self.random_state)

        if not self.warm_start or not hasattr(self, "estimators_"):
            # Free allocated memory, if any
            self.estimators_ = []

        n_more_estimators = self.n_estimators - len(self.estimators_)

        if n_more_estimators < 0:
            raise ValueError('n_estimators=%d must be larger or equal to '
                             'len(estimators_)=%d when warm_start==True'
                             % (self.n_estimators, len(self.estimators_)))

        elif n_more_estimators == 0:
            warn("Warm-start fitting without increasing n_estimators does not "
                 "fit new trees.")
        else:
            if self.warm_start and len(self.estimators_) > 0:
                # We draw from the random state to get the random state we
                # would have got if we hadn't used a warm_start.
                random_state.randint(MAX_INT, size=len(self.estimators_))

            trees = []
            for i in range(n_more_estimators):
                tree = self._make_estimator(append=False,
                                            random_state=random_state)
                trees.append(tree)

            # Parallel loop: we use the threading backend as the Cython code
            # for fitting the trees is internally releasing the Python GIL
            # making threading always more efficient than multiprocessing in
            # that case.
            trees = Parallel(n_jobs=self.n_jobs, verbose=self.verbose,
                             backend="threading")(
                delayed(_parallel_build_trees)(
                    t, self, X, y, sample_weight, i, len(trees),
                    verbose=self.verbose, class_weight=self.class_weight)
                for i, t in enumerate(trees))

            # Collect newly grown trees
            self.estimators_.extend(trees)

        if self.oob_score:
            self._set_oob_score(X, y)

        # Decapsulate classes_ attributes
        if hasattr(self, "classes_") and self.n_outputs_ == 1:
            self.n_classes_ = self.n_classes_[0]
            self.classes_ = self.classes_[0]

        return self

    @abstractmethod
    def _set_oob_score(self, X, y):
        """Calculate out of bag predictions and score."""

    def _validate_y_class_weight(self, y):
        # Default implementation
        return y, None

    def _validate_X_predict(self, X):
        """Validate X whenever one tries to predict, apply, predict_proba"""
        if self.estimators_ is None or len(self.estimators_) == 0:
            raise NotFittedError("Estimator not fitted, "
                                 "call `fit` before exploiting the model.")

        return self.estimators_[0]._validate_X_predict(X, check_input=True)

    @property
    def feature_importances_(self):
        """Return the feature importances (the higher, the more important the
           feature).

        Returns
        -------
        feature_importances_ : array, shape = [n_features]
        """
        check_is_fitted(self, 'estimators_')

        all_importances = Parallel(n_jobs=self.n_jobs,
                                   backend="threading")(
            delayed(getattr)(tree, 'feature_importances_')
            for tree in self.estimators_)

        return sum(all_importances) / len(self.estimators_)


# This is a utility function for joblib's Parallel. It can't go locally in
# ForestClassifier or ForestRegressor, because joblib complains that it cannot
# pickle it when placed there.

def accumulate_prediction(predict, X, out):
    prediction = predict(X, check_input=False)
    if len(out) == 1:
        out[0] += prediction
    else:
        for i in range(len(out)):
            out[i] += prediction[i]


class ForestClassifier(six.with_metaclass(ABCMeta, BaseForest,
                                          ClassifierMixin)):
    """Base class for forest of trees-based classifiers.

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

    @abstractmethod
    def __init__(self,
                 base_estimator,
                 n_estimators=10,
                 estimator_params=tuple(),
                 bootstrap=False,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False,
                 class_weight=None):

        super(ForestClassifier, self).__init__(
            base_estimator,
            n_estimators=n_estimators,
            estimator_params=estimator_params,
            bootstrap=bootstrap,
            oob_score=oob_score,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start,
            class_weight=class_weight)

    def _set_oob_score(self, X, y):
        """Compute out-of-bag score"""
        X = check_array(X, dtype=DTYPE, accept_sparse='csr')

        n_classes_ = self.n_classes_
        n_samples = y.shape[0]

        oob_decision_function = []
        oob_score = 0.0
        predictions = []

        for k in range(self.n_outputs_):
            predictions.append(np.zeros((n_samples, n_classes_[k])))

        for estimator in self.estimators_:
            unsampled_indices = _generate_unsampled_indices(
                estimator.random_state, n_samples)
            p_estimator = estimator.predict_proba(X[unsampled_indices, :],
                                                  check_input=False)

            if self.n_outputs_ == 1:
                p_estimator = [p_estimator]

            for k in range(self.n_outputs_):
                predictions[k][unsampled_indices, :] += p_estimator[k]

        for k in range(self.n_outputs_):
            if (predictions[k].sum(axis=1) == 0).any():
                warn("Some inputs do not have OOB scores. "
                     "This probably means too few trees were used "
                     "to compute any reliable oob estimates.")

            decision = (predictions[k] /
                        predictions[k].sum(axis=1)[:, np.newaxis])
            oob_decision_function.append(decision)
            oob_score += np.mean(y[:, k] ==
                                 np.argmax(predictions[k], axis=1), axis=0)

        if self.n_outputs_ == 1:
            self.oob_decision_function_ = oob_decision_function[0]
        else:
            self.oob_decision_function_ = oob_decision_function

        self.oob_score_ = oob_score / self.n_outputs_

    def _validate_y_class_weight(self, y):
        check_classification_targets(y)

        y = np.copy(y)
        expanded_class_weight = None

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

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

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

        if self.class_weight is not None:
            valid_presets = ('balanced', 'balanced_subsample')
            if isinstance(self.class_weight, six.string_types):
                if self.class_weight not in valid_presets:
                    raise ValueError('Valid presets for class_weight include '
                                     '"balanced" and "balanced_subsample". Given "%s".'
                                     % self.class_weight)
                if self.warm_start:
                    warn('class_weight presets "balanced" or "balanced_subsample" are '
                         'not recommended for warm_start if the fitted data '
                         'differs from the full dataset. In order to use '
                         '"balanced" weights, use compute_class_weight("balanced", '
                         'classes, y). In place of y you can use a large '
                         'enough sample of the full training set target to '
                         'properly estimate the class frequency '
                         'distributions. Pass the resulting weights as the '
                         'class_weight parameter.')

            if (self.class_weight != 'balanced_subsample' or
                    not self.bootstrap):
                if self.class_weight == "balanced_subsample":
                    class_weight = "balanced"
                else:
                    class_weight = self.class_weight
                expanded_class_weight = compute_sample_weight(class_weight,
                                                              y_original)

        return y, expanded_class_weight

    def predict(self, X):
        """Predict class for X.

        The predicted class of an input sample is a vote by the trees in
        the forest, weighted by their probability estimates. That is,
        the predicted class is the one with highest mean probability
        estimate across the trees.

        Parameters
        ----------
        X : array-like or sparse matrix of shape = [n_samples, n_features]
            The input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csr_matrix``.

        Returns
        -------
        y : array of shape = [n_samples] or [n_samples, n_outputs]
            The predicted classes.
        """
        proba = self.predict_proba(X)

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

        else:
            n_samples = proba[0].shape[0]
            predictions = np.zeros((n_samples, self.n_outputs_))

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

            return predictions

    def predict_proba(self, X):
        """Predict class probabilities for X.

        The predicted class probabilities of an input sample are computed as
        the mean predicted class probabilities of the trees in the forest. The
        class probability of a single tree is the fraction of samples of the same
        class in a leaf.

        Parameters
        ----------
        X : array-like or sparse matrix of shape = [n_samples, n_features]
            The input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csr_matrix``.

        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 `classes_`.
        """
        check_is_fitted(self, 'estimators_')
        # Check data
        X = self._validate_X_predict(X)

        # Assign chunk of trees to jobs
        n_jobs, _, _ = _partition_estimators(self.n_estimators, self.n_jobs)

        # avoid storing the output of every estimator by summing them here
        all_proba = [np.zeros((X.shape[0], j), dtype=np.float64)
                     for j in np.atleast_1d(self.n_classes_)]
        Parallel(n_jobs=n_jobs, verbose=self.verbose, backend="threading")(
            delayed(accumulate_prediction)(e.predict_proba, X, all_proba)
            for e in self.estimators_)

        for proba in all_proba:
            proba /= len(self.estimators_)

        if len(all_proba) == 1:
            return all_proba[0]
        else:
            return all_proba

    def predict_log_proba(self, X):
        """Predict class log-probabilities for X.

        The predicted class log-probabilities of an input sample is computed as
        the log of the mean predicted class probabilities of the trees in the
        forest.

        Parameters
        ----------
        X : array-like or sparse matrix of shape = [n_samples, n_features]
            The input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csr_matrix``.

        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 `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


class ForestRegressor(six.with_metaclass(ABCMeta, BaseForest, RegressorMixin)):
    """Base class for forest of trees-based regressors.

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

    @abstractmethod
    def __init__(self,
                 base_estimator,
                 n_estimators=10,
                 estimator_params=tuple(),
                 bootstrap=False,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False):
        super(ForestRegressor, self).__init__(
            base_estimator,
            n_estimators=n_estimators,
            estimator_params=estimator_params,
            bootstrap=bootstrap,
            oob_score=oob_score,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start)

    def predict(self, X):
        """Predict regression target for X.

        The predicted regression target of an input sample is computed as the
        mean predicted regression targets of the trees in the forest.

        Parameters
        ----------
        X : array-like or sparse matrix of shape = [n_samples, n_features]
            The input samples. Internally, its dtype will be converted to
            ``dtype=np.float32``. If a sparse matrix is provided, it will be
            converted into a sparse ``csr_matrix``.

        Returns
        -------
        y : array of shape = [n_samples] or [n_samples, n_outputs]
            The predicted values.
        """
        check_is_fitted(self, 'estimators_')
        # Check data
        X = self._validate_X_predict(X)

        # Assign chunk of trees to jobs
        n_jobs, _, _ = _partition_estimators(self.n_estimators, self.n_jobs)

        # avoid storing the output of every estimator by summing them here
        if self.n_outputs_ > 1:
            y_hat = np.zeros((X.shape[0], self.n_outputs_), dtype=np.float64)
        else:
            y_hat = np.zeros((X.shape[0]), dtype=np.float64)

        # Parallel loop
        Parallel(n_jobs=n_jobs, verbose=self.verbose, backend="threading")(
            delayed(accumulate_prediction)(e.predict, X, [y_hat])
            for e in self.estimators_)

        y_hat /= len(self.estimators_)

        return y_hat

    def _set_oob_score(self, X, y):
        """Compute out-of-bag scores"""
        X = check_array(X, dtype=DTYPE, accept_sparse='csr')

        n_samples = y.shape[0]

        predictions = np.zeros((n_samples, self.n_outputs_))
        n_predictions = np.zeros((n_samples, self.n_outputs_))

        for estimator in self.estimators_:
            unsampled_indices = _generate_unsampled_indices(
                estimator.random_state, n_samples)
            p_estimator = estimator.predict(
                X[unsampled_indices, :], check_input=False)

            if self.n_outputs_ == 1:
                p_estimator = p_estimator[:, np.newaxis]

            predictions[unsampled_indices, :] += p_estimator
            n_predictions[unsampled_indices, :] += 1

        if (n_predictions == 0).any():
            warn("Some inputs do not have OOB scores. "
                 "This probably means too few trees were used "
                 "to compute any reliable oob estimates.")
            n_predictions[n_predictions == 0] = 1

        predictions /= n_predictions
        self.oob_prediction_ = predictions

        if self.n_outputs_ == 1:
            self.oob_prediction_ = \
                self.oob_prediction_.reshape((n_samples, ))

        self.oob_score_ = 0.0

        for k in range(self.n_outputs_):
            self.oob_score_ += r2_score(y[:, k],
                                        predictions[:, k])

        self.oob_score_ /= self.n_outputs_


class RandomForestClassifier(ForestClassifier):
    """A random forest classifier.

    A random forest is a meta estimator that fits a number of decision tree
    classifiers on various sub-samples of the dataset and use averaging to
    improve the predictive accuracy and control over-fitting.
    The sub-sample size is always the same as the original
    input sample size but the samples are drawn with replacement if
    `bootstrap=True` (default).

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

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        The number of trees in the forest.

    criterion : string, optional (default="gini")
        The function to measure the quality of a split. Supported criteria are
        "gini" for the Gini impurity and "entropy" for the information gain.
        Note: this parameter is tree-specific.

    max_features : int, float, string or None, optional (default="auto")
        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 percentage and
          `int(max_features * n_features)` features are considered at each
          split.
        - If "auto", then `max_features=sqrt(n_features)`.
        - If "sqrt", then `max_features=sqrt(n_features)` (same as "auto").
        - 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.

    max_depth : integer or None, optional (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, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

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

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:

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

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

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees 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, optional (default=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

    bootstrap : boolean, optional (default=True)
        Whether bootstrap samples are used when building trees.

    oob_score : bool (default=False)
        Whether to use out-of-bag samples to estimate
        the generalization accuracy.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    random_state : int, RandomState instance or None, optional (default=None)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`.

    verbose : int, optional (default=0)
        Controls the verbosity of the tree building process.

    warm_start : bool, optional (default=False)
        When set to ``True``, reuse the solution of the previous call to fit
        and add more estimators to the ensemble, otherwise, just fit a whole
        new forest.

    class_weight : dict, list of dicts, "balanced",
        "balanced_subsample" or None, optional (default=None)
        Weights associated with classes in the form ``{class_label: weight}``.
        If not given, 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.

        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))``

        The "balanced_subsample" mode is the same as "balanced" except that
        weights are computed based on the bootstrap sample for every tree
        grown.

        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.

    Attributes
    ----------
    estimators_ : list of DecisionTreeClassifier
        The collection of fitted sub-estimators.

    classes_ : array of shape = [n_classes] or a list of such arrays
        The classes labels (single output problem), or a list of arrays of
        class labels (multi-output problem).

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

    n_features_ : int
        The number of features when ``fit`` is performed.

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

    feature_importances_ : array of shape = [n_features]
        The feature importances (the higher, the more important the feature).

    oob_score_ : float
        Score of the training dataset obtained using an out-of-bag estimate.

    oob_decision_function_ : array of shape = [n_samples, n_classes]
        Decision function computed with out-of-bag estimate on the training
        set. If n_estimators is small it might be possible that a data point
        was never left out during the bootstrap. In this case,
        `oob_decision_function_` might contain NaN.

    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 features are always randomly permuted at each split. Therefore,
    the best found split may vary, even with the same training data,
    ``max_features=n_features`` and ``bootstrap=False``, if the improvement
    of the criterion is identical for several splits enumerated during the
    search of the best split. To obtain a deterministic behaviour during
    fitting, ``random_state`` has to be fixed.

    References
    ----------

    .. [1] L. Breiman, "Random Forests", Machine Learning, 45(1), 5-32, 2001.

    See also
    --------
    DecisionTreeClassifier, ExtraTreesClassifier
    """
    def __init__(self,
                 n_estimators=10,
                 criterion="gini",
                 max_depth=None,
                 min_samples_split=2,
                 min_samples_leaf=1,
                 min_weight_fraction_leaf=0.,
                 max_features="auto",
                 max_leaf_nodes=None,
                 min_impurity_decrease=0.,
                 min_impurity_split=None,
                 bootstrap=True,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False,
                 class_weight=None):
        super(RandomForestClassifier, self).__init__(
            base_estimator=DecisionTreeClassifier(),
            n_estimators=n_estimators,
            estimator_params=("criterion", "max_depth", "min_samples_split",
                              "min_samples_leaf", "min_weight_fraction_leaf",
                              "max_features", "max_leaf_nodes",
                              "min_impurity_decrease", "min_impurity_split",
                              "random_state"),
            bootstrap=bootstrap,
            oob_score=oob_score,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start,
            class_weight=class_weight)

        self.criterion = criterion
        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.min_impurity_decrease = min_impurity_decrease
        self.min_impurity_split = min_impurity_split


class RandomForestRegressor(ForestRegressor):
    """A random forest regressor.

    A random forest is a meta estimator that fits a number of classifying
    decision trees on various sub-samples of the dataset and use averaging
    to improve the predictive accuracy and control over-fitting.
    The sub-sample size is always the same as the original
    input sample size but the samples are drawn with replacement if
    `bootstrap=True` (default).

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

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        The number of trees in the forest.

    criterion : string, optional (default="mse")
        The function to measure the quality of a split. Supported criteria
        are "mse" for the mean squared error, which is equal to variance
        reduction as feature selection criterion, and "mae" for the mean
        absolute error.

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

    max_features : int, float, string or None, optional (default="auto")
        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 percentage and
          `int(max_features * n_features)` features are considered at each
          split.
        - If "auto", then `max_features=n_features`.
        - 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.

    max_depth : integer or None, optional (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, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

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

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:

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

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

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees 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, optional (default=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

    bootstrap : boolean, optional (default=True)
        Whether bootstrap samples are used when building trees.

    oob_score : bool, optional (default=False)
        whether to use out-of-bag samples to estimate
        the R^2 on unseen data.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    random_state : int, RandomState instance or None, optional (default=None)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`.

    verbose : int, optional (default=0)
        Controls the verbosity of the tree building process.

    warm_start : bool, optional (default=False)
        When set to ``True``, reuse the solution of the previous call to fit
        and add more estimators to the ensemble, otherwise, just fit a whole
        new forest.

    Attributes
    ----------
    estimators_ : list of DecisionTreeRegressor
        The collection of fitted sub-estimators.

    feature_importances_ : array of shape = [n_features]
        The feature importances (the higher, the more important the feature).

    n_features_ : int
        The number of features when ``fit`` is performed.

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

    oob_score_ : float
        Score of the training dataset obtained using an out-of-bag estimate.

    oob_prediction_ : array of shape = [n_samples]
        Prediction computed with out-of-bag estimate on the training set.

    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 features are always randomly permuted at each split. Therefore,
    the best found split may vary, even with the same training data,
    ``max_features=n_features`` and ``bootstrap=False``, if the improvement
    of the criterion is identical for several splits enumerated during the
    search of the best split. To obtain a deterministic behaviour during
    fitting, ``random_state`` has to be fixed.

    References
    ----------

    .. [1] L. Breiman, "Random Forests", Machine Learning, 45(1), 5-32, 2001.

    See also
    --------
    DecisionTreeRegressor, ExtraTreesRegressor
    """
    def __init__(self,
                 n_estimators=10,
                 criterion="mse",
                 max_depth=None,
                 min_samples_split=2,
                 min_samples_leaf=1,
                 min_weight_fraction_leaf=0.,
                 max_features="auto",
                 max_leaf_nodes=None,
                 min_impurity_decrease=0.,
                 min_impurity_split=None,
                 bootstrap=True,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False):
        super(RandomForestRegressor, self).__init__(
            base_estimator=DecisionTreeRegressor(),
            n_estimators=n_estimators,
            estimator_params=("criterion", "max_depth", "min_samples_split",
                              "min_samples_leaf", "min_weight_fraction_leaf",
                              "max_features", "max_leaf_nodes",
                              "min_impurity_decrease", "min_impurity_split",
                              "random_state"),
            bootstrap=bootstrap,
            oob_score=oob_score,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start)

        self.criterion = criterion
        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.min_impurity_decrease = min_impurity_decrease
        self.min_impurity_split = min_impurity_split


class ExtraTreesClassifier(ForestClassifier):
    """An extra-trees classifier.

    This class implements a meta estimator that fits a number of
    randomized decision trees (a.k.a. extra-trees) on various sub-samples
    of the dataset and use averaging to improve the predictive accuracy
    and control over-fitting.

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

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        The number of trees in the forest.

    criterion : string, optional (default="gini")
        The function to measure the quality of a split. Supported criteria are
        "gini" for the Gini impurity and "entropy" for the information gain.

    max_features : int, float, string or None, optional (default="auto")
        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 percentage and
          `int(max_features * n_features)` features are considered at each
          split.
        - If "auto", then `max_features=sqrt(n_features)`.
        - 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.

    max_depth : integer or None, optional (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, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

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

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:

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

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

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees 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, optional (default=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

    bootstrap : boolean, optional (default=False)
        Whether bootstrap samples are used when building trees.

    oob_score : bool, optional (default=False)
        Whether to use out-of-bag samples to estimate
        the generalization accuracy.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    random_state : int, RandomState instance or None, optional (default=None)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`.

    verbose : int, optional (default=0)
        Controls the verbosity of the tree building process.

    warm_start : bool, optional (default=False)
        When set to ``True``, reuse the solution of the previous call to fit
        and add more estimators to the ensemble, otherwise, just fit a whole
        new forest.

    class_weight : dict, list of dicts, "balanced", "balanced_subsample" or None, optional (default=None)
        Weights associated with classes in the form ``{class_label: weight}``.
        If not given, 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.

        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))``

        The "balanced_subsample" mode is the same as "balanced" except that weights are
        computed based on the bootstrap sample for every tree grown.

        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.

    Attributes
    ----------
    estimators_ : list of DecisionTreeClassifier
        The collection of fitted sub-estimators.

    classes_ : array of shape = [n_classes] or a list of such arrays
        The classes labels (single output problem), or a list of arrays of
        class labels (multi-output problem).

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

    feature_importances_ : array of shape = [n_features]
        The feature importances (the higher, the more important the feature).

    n_features_ : int
        The number of features when ``fit`` is performed.

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

    oob_score_ : float
        Score of the training dataset obtained using an out-of-bag estimate.

    oob_decision_function_ : array of shape = [n_samples, n_classes]
        Decision function computed with out-of-bag estimate on the training
        set. If n_estimators is small it might be possible that a data point
        was never left out during the bootstrap. In this case,
        `oob_decision_function_` might contain NaN.

    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.

    See also
    --------
    sklearn.tree.ExtraTreeClassifier : Base classifier for this ensemble.
    RandomForestClassifier : Ensemble Classifier based on trees with optimal
        splits.
    """
    def __init__(self,
                 n_estimators=10,
                 criterion="gini",
                 max_depth=None,
                 min_samples_split=2,
                 min_samples_leaf=1,
                 min_weight_fraction_leaf=0.,
                 max_features="auto",
                 max_leaf_nodes=None,
                 min_impurity_decrease=0.,
                 min_impurity_split=None,
                 bootstrap=False,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False,
                 class_weight=None):
        super(ExtraTreesClassifier, self).__init__(
            base_estimator=ExtraTreeClassifier(),
            n_estimators=n_estimators,
            estimator_params=("criterion", "max_depth", "min_samples_split",
                              "min_samples_leaf", "min_weight_fraction_leaf",
                              "max_features", "max_leaf_nodes",
                              "min_impurity_decrease", "min_impurity_split",
                              "random_state"),
            bootstrap=bootstrap,
            oob_score=oob_score,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start,
            class_weight=class_weight)

        self.criterion = criterion
        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.min_impurity_decrease = min_impurity_decrease
        self.min_impurity_split = min_impurity_split


class ExtraTreesRegressor(ForestRegressor):
    """An extra-trees regressor.

    This class implements a meta estimator that fits a number of
    randomized decision trees (a.k.a. extra-trees) on various sub-samples
    of the dataset and use averaging to improve the predictive accuracy
    and control over-fitting.

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

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        The number of trees in the forest.

    criterion : string, optional (default="mse")
        The function to measure the quality of a split. Supported criteria
        are "mse" for the mean squared error, which is equal to variance
        reduction as feature selection criterion, and "mae" for the mean
        absolute error.

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

    max_features : int, float, string or None, optional (default="auto")
        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 percentage and
          `int(max_features * n_features)` features are considered at each
          split.
        - If "auto", then `max_features=n_features`.
        - 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.

    max_depth : integer or None, optional (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, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` are the minimum
          number of samples for each split.

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

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:

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

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

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees 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, optional (default=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

    bootstrap : boolean, optional (default=False)
        Whether bootstrap samples are used when building trees.

    oob_score : bool, optional (default=False)
        Whether to use out-of-bag samples to estimate the R^2 on unseen data.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    random_state : int, RandomState instance or None, optional (default=None)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`.

    verbose : int, optional (default=0)
        Controls the verbosity of the tree building process.

    warm_start : bool, optional (default=False)
        When set to ``True``, reuse the solution of the previous call to fit
        and add more estimators to the ensemble, otherwise, just fit a whole
        new forest.

    Attributes
    ----------
    estimators_ : list of DecisionTreeRegressor
        The collection of fitted sub-estimators.

    feature_importances_ : array of shape = [n_features]
        The feature importances (the higher, the more important the feature).

    n_features_ : int
        The number of features.

    n_outputs_ : int
        The number of outputs.

    oob_score_ : float
        Score of the training dataset obtained using an out-of-bag estimate.

    oob_prediction_ : array of shape = [n_samples]
        Prediction computed with out-of-bag estimate on the training set.

    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.

    See also
    --------
    sklearn.tree.ExtraTreeRegressor: Base estimator for this ensemble.
    RandomForestRegressor: Ensemble regressor using trees with optimal splits.
    """
    def __init__(self,
                 n_estimators=10,
                 criterion="mse",
                 max_depth=None,
                 min_samples_split=2,
                 min_samples_leaf=1,
                 min_weight_fraction_leaf=0.,
                 max_features="auto",
                 max_leaf_nodes=None,
                 min_impurity_decrease=0.,
                 min_impurity_split=None,
                 bootstrap=False,
                 oob_score=False,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False):
        super(ExtraTreesRegressor, self).__init__(
            base_estimator=ExtraTreeRegressor(),
            n_estimators=n_estimators,
            estimator_params=("criterion", "max_depth", "min_samples_split",
                              "min_samples_leaf", "min_weight_fraction_leaf",
                              "max_features", "max_leaf_nodes",
                              "min_impurity_decrease", "min_impurity_split",
                              "random_state"),
            bootstrap=bootstrap,
            oob_score=oob_score,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start)

        self.criterion = criterion
        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.min_impurity_decrease = min_impurity_decrease
        self.min_impurity_split = min_impurity_split


class RandomTreesEmbedding(BaseForest):
    """An ensemble of totally random trees.

    An unsupervised transformation of a dataset to a high-dimensional
    sparse representation. A datapoint is coded according to which leaf of
    each tree it is sorted into. Using a one-hot encoding of the leaves,
    this leads to a binary coding with as many ones as there are trees in
    the forest.

    The dimensionality of the resulting representation is
    ``n_out <= n_estimators * max_leaf_nodes``. If ``max_leaf_nodes == None``,
    the number of leaf nodes is at most ``n_estimators * 2 ** max_depth``.

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

    Parameters
    ----------
    n_estimators : integer, optional (default=10)
        Number of trees in the forest.

    max_depth : integer, optional (default=5)
        The maximum depth of each 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, float, optional (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 percentage and
          `ceil(min_samples_split * n_samples)` is the minimum
          number of samples for each split.

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

    min_samples_leaf : int, float, optional (default=1)
        The minimum number of samples required to be at a leaf node:

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

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

    min_weight_fraction_leaf : float, optional (default=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_leaf_nodes : int or None, optional (default=None)
        Grow trees 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, optional (default=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

    bootstrap : boolean, optional (default=True)
        Whether bootstrap samples are used when building trees.

    sparse_output : bool, optional (default=True)
        Whether or not to return a sparse CSR matrix, as default behavior,
        or to return a dense array compatible with dense pipeline operators.

    n_jobs : integer, optional (default=1)
        The number of jobs to run in parallel for both `fit` and `predict`.
        If -1, then the number of jobs is set to the number of cores.

    random_state : int, RandomState instance or None, optional (default=None)
        If int, random_state is the seed used by the random number generator;
        If RandomState instance, random_state is the random number generator;
        If None, the random number generator is the RandomState instance used
        by `np.random`.

    verbose : int, optional (default=0)
        Controls the verbosity of the tree building process.

    warm_start : bool, optional (default=False)
        When set to ``True``, reuse the solution of the previous call to fit
        and add more estimators to the ensemble, otherwise, just fit a whole
        new forest.

    Attributes
    ----------
    estimators_ : list of DecisionTreeClassifier
        The collection of fitted sub-estimators.

    References
    ----------
    .. [1] P. Geurts, D. Ernst., and L. Wehenkel, "Extremely randomized trees",
           Machine Learning, 63(1), 3-42, 2006.
    .. [2] Moosmann, F. and Triggs, B. and Jurie, F.  "Fast discriminative
           visual codebooks using randomized clustering forests"
           NIPS 2007

    """

    def __init__(self,
                 n_estimators=10,
                 max_depth=5,
                 min_samples_split=2,
                 min_samples_leaf=1,
                 min_weight_fraction_leaf=0.,
                 max_leaf_nodes=None,
                 min_impurity_decrease=0.,
                 min_impurity_split=None,
                 sparse_output=True,
                 n_jobs=1,
                 random_state=None,
                 verbose=0,
                 warm_start=False):
        super(RandomTreesEmbedding, self).__init__(
            base_estimator=ExtraTreeRegressor(),
            n_estimators=n_estimators,
            estimator_params=("criterion", "max_depth", "min_samples_split",
                              "min_samples_leaf", "min_weight_fraction_leaf",
                              "max_features", "max_leaf_nodes",
                              "min_impurity_decrease", "min_impurity_split",
                              "random_state"),
            bootstrap=False,
            oob_score=False,
            n_jobs=n_jobs,
            random_state=random_state,
            verbose=verbose,
            warm_start=warm_start)

        self.criterion = 'mse'
        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 = 1
        self.max_leaf_nodes = max_leaf_nodes
        self.min_impurity_decrease = min_impurity_decrease
        self.min_impurity_split = min_impurity_split
        self.sparse_output = sparse_output

    def _set_oob_score(self, X, y):
        raise NotImplementedError("OOB score not supported by tree embedding")

    def fit(self, X, y=None, sample_weight=None):
        """Fit estimator.

        Parameters
        ----------
        X : array-like or sparse matrix, shape=(n_samples, n_features)
            The input samples. Use ``dtype=np.float32`` for maximum
            efficiency. Sparse matrices are also supported, use sparse
            ``csc_matrix`` for maximum efficiency.

        Returns
        -------
        self : object
            Returns self.

        """
        self.fit_transform(X, y, sample_weight=sample_weight)
        return self

    def fit_transform(self, X, y=None, sample_weight=None):
        """Fit estimator and transform dataset.

        Parameters
        ----------
        X : array-like or sparse matrix, shape=(n_samples, n_features)
            Input data used to build forests. Use ``dtype=np.float32`` for
            maximum efficiency.

        Returns
        -------
        X_transformed : sparse matrix, shape=(n_samples, n_out)
            Transformed dataset.
        """
        X = check_array(X, accept_sparse=['csc'])
        if issparse(X):
            # Pre-sort indices to avoid that each individual tree of the
            # ensemble sorts the indices.
            X.sort_indices()

        rnd = check_random_state(self.random_state)
        y = rnd.uniform(size=X.shape[0])
        super(RandomTreesEmbedding, self).fit(X, y,
                                              sample_weight=sample_weight)

        self.one_hot_encoder_ = OneHotEncoder(sparse=self.sparse_output)
        return self.one_hot_encoder_.fit_transform(self.apply(X))

    def transform(self, X):
        """Transform dataset.

        Parameters
        ----------
        X : array-like or sparse matrix, shape=(n_samples, n_features)
            Input data to be transformed. Use ``dtype=np.float32`` for maximum
            efficiency. Sparse matrices are also supported, use sparse
            ``csr_matrix`` for maximum efficiency.

        Returns
        -------
        X_transformed : sparse matrix, shape=(n_samples, n_out)
            Transformed dataset.
        """
        return self.one_hot_encoder_.transform(self.apply(X))