content: """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_)
  
  
  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)
  
          # Parallel loop
          all_proba = Parallel(n_jobs=n_jobs, verbose=self.verbose,
                               backend="threading")(
              delayed(parallel_helper)(e, 'predict_proba', X,
                                        check_input=False)
              for e in self.estimators_)
  
          # Reduce
          proba = all_proba[0]
  
          if self.n_outputs_ == 1:
              for j in range(1, len(all_proba)):
                  proba += all_proba[j]
  
              proba /= len(self.estimators_)
  
          else:
              for j in range(1, len(all_proba)):
                  for k in range(self.n_outputs_):
                      proba[k] += all_proba[j][k]
  
              for k in range(self.n_outputs_):
                  proba[k] /= self.n_estimators
  
          return 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)
  
          # Parallel loop
          all_y_hat = Parallel(n_jobs=n_jobs, verbose=self.verbose,
                               backend="threading")(
              delayed(parallel_helper)(e, 'predict', X, check_input=False)
              for e in self.estimators_)
  
          # Reduce
          y_hat = sum(all_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_split : float, optional (default=1e-7)
          Threshold for early stopping in tree growth. A node will split
          if its impurity is above the threshold, otherwise it is a leaf.
  
          .. versionadded:: 0.18
  
      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 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_split=1e-7,
                   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_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_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_split : float, optional (default=1e-7)
          Threshold for early stopping in tree growth. A node will split
          if its impurity is above the threshold, otherwise it is a leaf.
  
          .. versionadded:: 0.18
  
      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 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_split=1e-7,
                   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_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_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_split : float, optional (default=1e-7)
          Threshold for early stopping in tree growth. A node will split
          if its impurity is above the threshold, otherwise it is a leaf.
  
          .. versionadded:: 0.18
  
      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.
  
      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_split=1e-7,
                   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_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_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_split : float, optional (default=1e-7)
          Threshold for early stopping in tree growth. A node will split
          if its impurity is above the threshold, otherwise it is a leaf.
  
          .. versionadded:: 0.18
  
      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.
  
      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_split=1e-7,
                   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_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_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_split : float, optional (default=1e-7)
          Threshold for early stopping in tree growth. A node will split
          if its impurity is above the threshold, otherwise it is a leaf.
  
          .. versionadded:: 0.18
  
      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_split=1e-7,
                   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_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_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))
  