content: """Gradient Boosted Regression Trees
  
  This module contains methods for fitting gradient boosted regression trees for
  both classification and regression.
  
  The module structure is the following:
  
  - The ``BaseGradientBoosting`` base class implements a common ``fit`` method
    for all the estimators in the module. Regression and classification
    only differ in the concrete ``LossFunction`` used.
  
  - ``GradientBoostingClassifier`` implements gradient boosting for
    classification problems.
  
  - ``GradientBoostingRegressor`` implements gradient boosting for
    regression problems.
  """
  
  # Authors: Peter Prettenhofer, Scott White, Gilles Louppe, Emanuele Olivetti,
  #          Arnaud Joly, Jacob Schreiber
  # License: BSD 3 clause
  
  from __future__ import print_function
  from __future__ import division
  
  from abc import ABCMeta
  from abc import abstractmethod
  
  from .base import BaseEnsemble
  from ..base import BaseEstimator
  from ..base import ClassifierMixin
  from ..base import RegressorMixin
  from ..externals import six
  
  from ._gradient_boosting import predict_stages
  from ._gradient_boosting import predict_stage
  from ._gradient_boosting import _random_sample_mask
  
  import numbers
  import numpy as np
  
  from scipy import stats
  from scipy.sparse import csc_matrix
  from scipy.sparse import csr_matrix
  from scipy.sparse import issparse
  
  from time import time
  from ..tree.tree import DecisionTreeRegressor
  from ..tree._tree import DTYPE
  from ..tree._tree import TREE_LEAF
  
  from ..utils import check_random_state
  from ..utils import check_array
  from ..utils import check_X_y
  from ..utils import column_or_1d
  from ..utils import check_consistent_length
  from ..utils.extmath import logsumexp
  from ..utils.fixes import expit
  from ..utils.fixes import bincount
  from ..utils import deprecated
  from ..utils.stats import _weighted_percentile
  from ..utils.validation import check_is_fitted
  from ..utils.multiclass import check_classification_targets
  from ..exceptions import NotFittedError
  
  
  class QuantileEstimator(BaseEstimator):
      """An estimator predicting the alpha-quantile of the training targets."""
      def __init__(self, alpha=0.9):
          if not 0 < alpha < 1.0:
              raise ValueError("`alpha` must be in (0, 1.0) but was %r" % alpha)
          self.alpha = alpha
  
      def fit(self, X, y, sample_weight=None):
          if sample_weight is None:
              self.quantile = stats.scoreatpercentile(y, self.alpha * 100.0)
          else:
              self.quantile = _weighted_percentile(y, sample_weight,
                                                   self.alpha * 100.0)
  
      def predict(self, X):
          check_is_fitted(self, 'quantile')
  
          y = np.empty((X.shape[0], 1), dtype=np.float64)
          y.fill(self.quantile)
          return y
  
  
  class MeanEstimator(BaseEstimator):
      """An estimator predicting the mean of the training targets."""
      def fit(self, X, y, sample_weight=None):
          if sample_weight is None:
              self.mean = np.mean(y)
          else:
              self.mean = np.average(y, weights=sample_weight)
  
      def predict(self, X):
          check_is_fitted(self, 'mean')
  
          y = np.empty((X.shape[0], 1), dtype=np.float64)
          y.fill(self.mean)
          return y
  
  
  class LogOddsEstimator(BaseEstimator):
      """An estimator predicting the log odds ratio."""
      scale = 1.0
  
      def fit(self, X, y, sample_weight=None):
          # pre-cond: pos, neg are encoded as 1, 0
          if sample_weight is None:
              pos = np.sum(y)
              neg = y.shape[0] - pos
          else:
              pos = np.sum(sample_weight * y)
              neg = np.sum(sample_weight * (1 - y))
  
          if neg == 0 or pos == 0:
              raise ValueError('y contains non binary labels.')
          self.prior = self.scale * np.log(pos / neg)
  
      def predict(self, X):
          check_is_fitted(self, 'prior')
  
          y = np.empty((X.shape[0], 1), dtype=np.float64)
          y.fill(self.prior)
          return y
  
  
  class ScaledLogOddsEstimator(LogOddsEstimator):
      """Log odds ratio scaled by 0.5 -- for exponential loss. """
      scale = 0.5
  
  
  class PriorProbabilityEstimator(BaseEstimator):
      """An estimator predicting the probability of each
      class in the training data.
      """
      def fit(self, X, y, sample_weight=None):
          if sample_weight is None:
              sample_weight = np.ones_like(y, dtype=np.float64)
          class_counts = bincount(y, weights=sample_weight)
          self.priors = class_counts / class_counts.sum()
  
      def predict(self, X):
          check_is_fitted(self, 'priors')
  
          y = np.empty((X.shape[0], self.priors.shape[0]), dtype=np.float64)
          y[:] = self.priors
          return y
  
  
  class ZeroEstimator(BaseEstimator):
      """An estimator that simply predicts zero. """
  
      def fit(self, X, y, sample_weight=None):
          if np.issubdtype(y.dtype, int):
              # classification
              self.n_classes = np.unique(y).shape[0]
              if self.n_classes == 2:
                  self.n_classes = 1
          else:
              # regression
              self.n_classes = 1
  
      def predict(self, X):
          check_is_fitted(self, 'n_classes')
  
          y = np.empty((X.shape[0], self.n_classes), dtype=np.float64)
          y.fill(0.0)
          return y
  
  
  class LossFunction(six.with_metaclass(ABCMeta, object)):
      """Abstract base class for various loss functions.
  
      Attributes
      ----------
      K : int
          The number of regression trees to be induced;
          1 for regression and binary classification;
          ``n_classes`` for multi-class classification.
      """
  
      is_multi_class = False
  
      def __init__(self, n_classes):
          self.K = n_classes
  
      def init_estimator(self):
          """Default ``init`` estimator for loss function. """
          raise NotImplementedError()
  
      @abstractmethod
      def __call__(self, y, pred, sample_weight=None):
          """Compute the loss of prediction ``pred`` and ``y``. """
  
      @abstractmethod
      def negative_gradient(self, y, y_pred, **kargs):
          """Compute the negative gradient.
  
          Parameters
          ---------
          y : np.ndarray, shape=(n,)
              The target labels.
          y_pred : np.ndarray, shape=(n,):
              The predictions.
          """
  
      def update_terminal_regions(self, tree, X, y, residual, y_pred,
                                  sample_weight, sample_mask,
                                  learning_rate=1.0, k=0):
          """Update the terminal regions (=leaves) of the given tree and
          updates the current predictions of the model. Traverses tree
          and invokes template method `_update_terminal_region`.
  
          Parameters
          ----------
          tree : tree.Tree
              The tree object.
          X : ndarray, shape=(n, m)
              The data array.
          y : ndarray, shape=(n,)
              The target labels.
          residual : ndarray, shape=(n,)
              The residuals (usually the negative gradient).
          y_pred : ndarray, shape=(n,)
              The predictions.
          sample_weight : ndarray, shape=(n,)
              The weight of each sample.
          sample_mask : ndarray, shape=(n,)
              The sample mask to be used.
          learning_rate : float, default=0.1
              learning rate shrinks the contribution of each tree by
               ``learning_rate``.
          k : int, default 0
              The index of the estimator being updated.
  
          """
          # compute leaf for each sample in ``X``.
          terminal_regions = tree.apply(X)
  
          # mask all which are not in sample mask.
          masked_terminal_regions = terminal_regions.copy()
          masked_terminal_regions[~sample_mask] = -1
  
          # update each leaf (= perform line search)
          for leaf in np.where(tree.children_left == TREE_LEAF)[0]:
              self._update_terminal_region(tree, masked_terminal_regions,
                                           leaf, X, y, residual,
                                           y_pred[:, k], sample_weight)
  
          # update predictions (both in-bag and out-of-bag)
          y_pred[:, k] += (learning_rate
                           * tree.value[:, 0, 0].take(terminal_regions, axis=0))
  
      @abstractmethod
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          """Template method for updating terminal regions (=leaves). """
  
  
  class RegressionLossFunction(six.with_metaclass(ABCMeta, LossFunction)):
      """Base class for regression loss functions. """
  
      def __init__(self, n_classes):
          if n_classes != 1:
              raise ValueError("``n_classes`` must be 1 for regression but "
                               "was %r" % n_classes)
          super(RegressionLossFunction, self).__init__(n_classes)
  
  
  class LeastSquaresError(RegressionLossFunction):
      """Loss function for least squares (LS) estimation.
      Terminal regions need not to be updated for least squares. """
      def init_estimator(self):
          return MeanEstimator()
  
      def __call__(self, y, pred, sample_weight=None):
          if sample_weight is None:
              return np.mean((y - pred.ravel()) ** 2.0)
          else:
              return (1.0 / sample_weight.sum() *
                      np.sum(sample_weight * ((y - pred.ravel()) ** 2.0)))
  
      def negative_gradient(self, y, pred, **kargs):
          return y - pred.ravel()
  
      def update_terminal_regions(self, tree, X, y, residual, y_pred,
                                  sample_weight, sample_mask,
                                  learning_rate=1.0, k=0):
          """Least squares does not need to update terminal regions.
  
          But it has to update the predictions.
          """
          # update predictions
          y_pred[:, k] += learning_rate * tree.predict(X).ravel()
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          pass
  
  
  class LeastAbsoluteError(RegressionLossFunction):
      """Loss function for least absolute deviation (LAD) regression. """
      def init_estimator(self):
          return QuantileEstimator(alpha=0.5)
  
      def __call__(self, y, pred, sample_weight=None):
          if sample_weight is None:
              return np.abs(y - pred.ravel()).mean()
          else:
              return (1.0 / sample_weight.sum() *
                      np.sum(sample_weight * np.abs(y - pred.ravel())))
  
      def negative_gradient(self, y, pred, **kargs):
          """1.0 if y - pred > 0.0 else -1.0"""
          pred = pred.ravel()
          return 2.0 * (y - pred > 0.0) - 1.0
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          """LAD updates terminal regions to median estimates. """
          terminal_region = np.where(terminal_regions == leaf)[0]
          sample_weight = sample_weight.take(terminal_region, axis=0)
          diff = y.take(terminal_region, axis=0) - pred.take(terminal_region, axis=0)
          tree.value[leaf, 0, 0] = _weighted_percentile(diff, sample_weight, percentile=50)
  
  
  class HuberLossFunction(RegressionLossFunction):
      """Huber loss function for robust regression.
  
      M-Regression proposed in Friedman 2001.
  
      References
      ----------
      J. Friedman, Greedy Function Approximation: A Gradient Boosting
      Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.
      """
  
      def __init__(self, n_classes, alpha=0.9):
          super(HuberLossFunction, self).__init__(n_classes)
          self.alpha = alpha
          self.gamma = None
  
      def init_estimator(self):
          return QuantileEstimator(alpha=0.5)
  
      def __call__(self, y, pred, sample_weight=None):
          pred = pred.ravel()
          diff = y - pred
          gamma = self.gamma
          if gamma is None:
              if sample_weight is None:
                  gamma = stats.scoreatpercentile(np.abs(diff), self.alpha * 100)
              else:
                  gamma = _weighted_percentile(np.abs(diff), sample_weight, self.alpha * 100)
  
          gamma_mask = np.abs(diff) <= gamma
          if sample_weight is None:
              sq_loss = np.sum(0.5 * diff[gamma_mask] ** 2.0)
              lin_loss = np.sum(gamma * (np.abs(diff[~gamma_mask]) - gamma / 2.0))
              loss = (sq_loss + lin_loss) / y.shape[0]
          else:
              sq_loss = np.sum(0.5 * sample_weight[gamma_mask] * diff[gamma_mask] ** 2.0)
              lin_loss = np.sum(gamma * sample_weight[~gamma_mask] *
                                (np.abs(diff[~gamma_mask]) - gamma / 2.0))
              loss = (sq_loss + lin_loss) / sample_weight.sum()
          return loss
  
      def negative_gradient(self, y, pred, sample_weight=None, **kargs):
          pred = pred.ravel()
          diff = y - pred
          if sample_weight is None:
              gamma = stats.scoreatpercentile(np.abs(diff), self.alpha * 100)
          else:
              gamma = _weighted_percentile(np.abs(diff), sample_weight, self.alpha * 100)
          gamma_mask = np.abs(diff) <= gamma
          residual = np.zeros((y.shape[0],), dtype=np.float64)
          residual[gamma_mask] = diff[gamma_mask]
          residual[~gamma_mask] = gamma * np.sign(diff[~gamma_mask])
          self.gamma = gamma
          return residual
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          terminal_region = np.where(terminal_regions == leaf)[0]
          sample_weight = sample_weight.take(terminal_region, axis=0)
          gamma = self.gamma
          diff = (y.take(terminal_region, axis=0)
                  - pred.take(terminal_region, axis=0))
          median = _weighted_percentile(diff, sample_weight, percentile=50)
          diff_minus_median = diff - median
          tree.value[leaf, 0] = median + np.mean(
              np.sign(diff_minus_median) *
              np.minimum(np.abs(diff_minus_median), gamma))
  
  
  class QuantileLossFunction(RegressionLossFunction):
      """Loss function for quantile regression.
  
      Quantile regression allows to estimate the percentiles
      of the conditional distribution of the target.
      """
  
      def __init__(self, n_classes, alpha=0.9):
          super(QuantileLossFunction, self).__init__(n_classes)
          assert 0 < alpha < 1.0
          self.alpha = alpha
          self.percentile = alpha * 100.0
  
      def init_estimator(self):
          return QuantileEstimator(self.alpha)
  
      def __call__(self, y, pred, sample_weight=None):
          pred = pred.ravel()
          diff = y - pred
          alpha = self.alpha
  
          mask = y > pred
          if sample_weight is None:
              loss = (alpha * diff[mask].sum() -
                      (1.0 - alpha) * diff[~mask].sum()) / y.shape[0]
          else:
              loss = ((alpha * np.sum(sample_weight[mask] * diff[mask]) -
                      (1.0 - alpha) * np.sum(sample_weight[~mask] * diff[~mask])) /
                      sample_weight.sum())
          return loss
  
      def negative_gradient(self, y, pred, **kargs):
          alpha = self.alpha
          pred = pred.ravel()
          mask = y > pred
          return (alpha * mask) - ((1.0 - alpha) * ~mask)
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          terminal_region = np.where(terminal_regions == leaf)[0]
          diff = (y.take(terminal_region, axis=0)
                  - pred.take(terminal_region, axis=0))
          sample_weight = sample_weight.take(terminal_region, axis=0)
  
          val = _weighted_percentile(diff, sample_weight, self.percentile)
          tree.value[leaf, 0] = val
  
  
  class ClassificationLossFunction(six.with_metaclass(ABCMeta, LossFunction)):
      """Base class for classification loss functions. """
  
      def _score_to_proba(self, score):
          """Template method to convert scores to probabilities.
  
           the does not support probabilites raises AttributeError.
          """
          raise TypeError('%s does not support predict_proba' % type(self).__name__)
  
      @abstractmethod
      def _score_to_decision(self, score):
          """Template method to convert scores to decisions.
  
          Returns int arrays.
          """
  
  
  class BinomialDeviance(ClassificationLossFunction):
      """Binomial deviance loss function for binary classification.
  
      Binary classification is a special case; here, we only need to
      fit one tree instead of ``n_classes`` trees.
      """
      def __init__(self, n_classes):
          if n_classes != 2:
              raise ValueError("{0:s} requires 2 classes.".format(
                  self.__class__.__name__))
          # we only need to fit one tree for binary clf.
          super(BinomialDeviance, self).__init__(1)
  
      def init_estimator(self):
          return LogOddsEstimator()
  
      def __call__(self, y, pred, sample_weight=None):
          """Compute the deviance (= 2 * negative log-likelihood). """
          # logaddexp(0, v) == log(1.0 + exp(v))
          pred = pred.ravel()
          if sample_weight is None:
              return -2.0 * np.mean((y * pred) - np.logaddexp(0.0, pred))
          else:
              return (-2.0 / sample_weight.sum() *
                      np.sum(sample_weight * ((y * pred) - np.logaddexp(0.0, pred))))
  
      def negative_gradient(self, y, pred, **kargs):
          """Compute the residual (= negative gradient). """
          return y - expit(pred.ravel())
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          """Make a single Newton-Raphson step.
  
          our node estimate is given by:
  
              sum(w * (y - prob)) / sum(w * prob * (1 - prob))
  
          we take advantage that: y - prob = residual
          """
          terminal_region = np.where(terminal_regions == leaf)[0]
          residual = residual.take(terminal_region, axis=0)
          y = y.take(terminal_region, axis=0)
          sample_weight = sample_weight.take(terminal_region, axis=0)
  
          numerator = np.sum(sample_weight * residual)
          denominator = np.sum(sample_weight * (y - residual) * (1 - y + residual))
  
          if denominator == 0.0:
              tree.value[leaf, 0, 0] = 0.0
          else:
              tree.value[leaf, 0, 0] = numerator / denominator
  
      def _score_to_proba(self, score):
          proba = np.ones((score.shape[0], 2), dtype=np.float64)
          proba[:, 1] = expit(score.ravel())
          proba[:, 0] -= proba[:, 1]
          return proba
  
      def _score_to_decision(self, score):
          proba = self._score_to_proba(score)
          return np.argmax(proba, axis=1)
  
  
  class MultinomialDeviance(ClassificationLossFunction):
      """Multinomial deviance loss function for multi-class classification.
  
      For multi-class classification we need to fit ``n_classes`` trees at
      each stage.
      """
  
      is_multi_class = True
  
      def __init__(self, n_classes):
          if n_classes < 3:
              raise ValueError("{0:s} requires more than 2 classes.".format(
                  self.__class__.__name__))
          super(MultinomialDeviance, self).__init__(n_classes)
  
      def init_estimator(self):
          return PriorProbabilityEstimator()
  
      def __call__(self, y, pred, sample_weight=None):
          # create one-hot label encoding
          Y = np.zeros((y.shape[0], self.K), dtype=np.float64)
          for k in range(self.K):
              Y[:, k] = y == k
  
          if sample_weight is None:
              return np.sum(-1 * (Y * pred).sum(axis=1) +
                            logsumexp(pred, axis=1))
          else:
              return np.sum(-1 * sample_weight * (Y * pred).sum(axis=1) +
                            logsumexp(pred, axis=1))
  
      def negative_gradient(self, y, pred, k=0, **kwargs):
          """Compute negative gradient for the ``k``-th class. """
          return y - np.nan_to_num(np.exp(pred[:, k] -
                                          logsumexp(pred, axis=1)))
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          """Make a single Newton-Raphson step. """
          terminal_region = np.where(terminal_regions == leaf)[0]
          residual = residual.take(terminal_region, axis=0)
          y = y.take(terminal_region, axis=0)
          sample_weight = sample_weight.take(terminal_region, axis=0)
  
          numerator = np.sum(sample_weight * residual)
          numerator *= (self.K - 1) / self.K
  
          denominator = np.sum(sample_weight * (y - residual) *
                               (1.0 - y + residual))
  
          if denominator == 0.0:
              tree.value[leaf, 0, 0] = 0.0
          else:
              tree.value[leaf, 0, 0] = numerator / denominator
  
      def _score_to_proba(self, score):
          return np.nan_to_num(
              np.exp(score - (logsumexp(score, axis=1)[:, np.newaxis])))
  
      def _score_to_decision(self, score):
          proba = self._score_to_proba(score)
          return np.argmax(proba, axis=1)
  
  
  class ExponentialLoss(ClassificationLossFunction):
      """Exponential loss function for binary classification.
  
      Same loss as AdaBoost.
  
      References
      ----------
      Greg Ridgeway, Generalized Boosted Models: A guide to the gbm package, 2007
      """
      def __init__(self, n_classes):
          if n_classes != 2:
              raise ValueError("{0:s} requires 2 classes.".format(
                  self.__class__.__name__))
          # we only need to fit one tree for binary clf.
          super(ExponentialLoss, self).__init__(1)
  
      def init_estimator(self):
          return ScaledLogOddsEstimator()
  
      def __call__(self, y, pred, sample_weight=None):
          pred = pred.ravel()
          if sample_weight is None:
              return np.mean(np.exp(-(2. * y - 1.) * pred))
          else:
              return (1.0 / sample_weight.sum() *
                      np.sum(sample_weight * np.exp(-(2 * y - 1) * pred)))
  
      def negative_gradient(self, y, pred, **kargs):
          y_ = -(2. * y - 1.)
          return y_ * np.exp(y_ * pred.ravel())
  
      def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
                                  residual, pred, sample_weight):
          terminal_region = np.where(terminal_regions == leaf)[0]
          pred = pred.take(terminal_region, axis=0)
          y = y.take(terminal_region, axis=0)
          sample_weight = sample_weight.take(terminal_region, axis=0)
  
          y_ = 2. * y - 1.
  
          numerator = np.sum(y_ * sample_weight * np.exp(-y_ * pred))
          denominator = np.sum(sample_weight * np.exp(-y_ * pred))
  
          if denominator == 0.0:
              tree.value[leaf, 0, 0] = 0.0
          else:
              tree.value[leaf, 0, 0] = numerator / denominator
  
      def _score_to_proba(self, score):
          proba = np.ones((score.shape[0], 2), dtype=np.float64)
          proba[:, 1] = expit(2.0 * score.ravel())
          proba[:, 0] -= proba[:, 1]
          return proba
  
      def _score_to_decision(self, score):
          return (score.ravel() >= 0.0).astype(np.int)
  
  
  LOSS_FUNCTIONS = {'ls': LeastSquaresError,
                    'lad': LeastAbsoluteError,
                    'huber': HuberLossFunction,
                    'quantile': QuantileLossFunction,
                    'deviance': None,    # for both, multinomial and binomial
                    'exponential': ExponentialLoss,
                    }
  
  
  INIT_ESTIMATORS = {'zero': ZeroEstimator}
  
  
  class VerboseReporter(object):
      """Reports verbose output to stdout.
  
      If ``verbose==1`` output is printed once in a while (when iteration mod
      verbose_mod is zero).; if larger than 1 then output is printed for
      each update.
      """
  
      def __init__(self, verbose):
          self.verbose = verbose
  
      def init(self, est, begin_at_stage=0):
          # header fields and line format str
          header_fields = ['Iter', 'Train Loss']
          verbose_fmt = ['{iter:>10d}', '{train_score:>16.4f}']
          # do oob?
          if est.subsample < 1:
              header_fields.append('OOB Improve')
              verbose_fmt.append('{oob_impr:>16.4f}')
          header_fields.append('Remaining Time')
          verbose_fmt.append('{remaining_time:>16s}')
  
          # print the header line
          print(('%10s ' + '%16s ' *
                 (len(header_fields) - 1)) % tuple(header_fields))
  
          self.verbose_fmt = ' '.join(verbose_fmt)
          # plot verbose info each time i % verbose_mod == 0
          self.verbose_mod = 1
          self.start_time = time()
          self.begin_at_stage = begin_at_stage
  
      def update(self, j, est):
          """Update reporter with new iteration. """
          do_oob = est.subsample < 1
          # we need to take into account if we fit additional estimators.
          i = j - self.begin_at_stage  # iteration relative to the start iter
          if (i + 1) % self.verbose_mod == 0:
              oob_impr = est.oob_improvement_[j] if do_oob else 0
              remaining_time = ((est.n_estimators - (j + 1)) *
                                (time() - self.start_time) / float(i + 1))
              if remaining_time > 60:
                  remaining_time = '{0:.2f}m'.format(remaining_time / 60.0)
              else:
                  remaining_time = '{0:.2f}s'.format(remaining_time)
              print(self.verbose_fmt.format(iter=j + 1,
                                            train_score=est.train_score_[j],
                                            oob_impr=oob_impr,
                                            remaining_time=remaining_time))
              if self.verbose == 1 and ((i + 1) // (self.verbose_mod * 10) > 0):
                  # adjust verbose frequency (powers of 10)
                  self.verbose_mod *= 10
  
  
  class BaseGradientBoosting(six.with_metaclass(ABCMeta, BaseEnsemble)):
      """Abstract base class for Gradient Boosting. """
  
      @abstractmethod
      def __init__(self, loss, learning_rate, n_estimators, criterion,
                   min_samples_split, min_samples_leaf, min_weight_fraction_leaf,
                   max_depth, min_impurity_split, init, subsample, max_features,
                   random_state, alpha=0.9, verbose=0, max_leaf_nodes=None,
                   warm_start=False, presort='auto'):
  
          self.n_estimators = n_estimators
          self.learning_rate = learning_rate
          self.loss = loss
          self.criterion = criterion
          self.min_samples_split = min_samples_split
          self.min_samples_leaf = min_samples_leaf
          self.min_weight_fraction_leaf = min_weight_fraction_leaf
          self.subsample = subsample
          self.max_features = max_features
          self.max_depth = max_depth
          self.min_impurity_split = min_impurity_split
          self.init = init
          self.random_state = random_state
          self.alpha = alpha
          self.verbose = verbose
          self.max_leaf_nodes = max_leaf_nodes
          self.warm_start = warm_start
          self.presort = presort
  
      def _fit_stage(self, i, X, y, y_pred, sample_weight, sample_mask,
                     random_state, X_idx_sorted, X_csc=None, X_csr=None):
          """Fit another stage of ``n_classes_`` trees to the boosting model. """
  
          assert sample_mask.dtype == np.bool
          loss = self.loss_
          original_y = y
  
          for k in range(loss.K):
              if loss.is_multi_class:
                  y = np.array(original_y == k, dtype=np.float64)
  
              residual = loss.negative_gradient(y, y_pred, k=k,
                                                sample_weight=sample_weight)
  
              # induce regression tree on residuals
              tree = DecisionTreeRegressor(
                  criterion=self.criterion,
                  splitter='best',
                  max_depth=self.max_depth,
                  min_samples_split=self.min_samples_split,
                  min_samples_leaf=self.min_samples_leaf,
                  min_weight_fraction_leaf=self.min_weight_fraction_leaf,
                  min_impurity_split=self.min_impurity_split,
                  max_features=self.max_features,
                  max_leaf_nodes=self.max_leaf_nodes,
                  random_state=random_state,
                  presort=self.presort)
  
              if self.subsample < 1.0:
                  # no inplace multiplication!
                  sample_weight = sample_weight * sample_mask.astype(np.float64)
  
              if X_csc is not None:
                  tree.fit(X_csc, residual, sample_weight=sample_weight,
                           check_input=False, X_idx_sorted=X_idx_sorted)
              else:
                  tree.fit(X, residual, sample_weight=sample_weight,
                           check_input=False, X_idx_sorted=X_idx_sorted)
  
              # update tree leaves
              if X_csr is not None:
                  loss.update_terminal_regions(tree.tree_, X_csr, y, residual, y_pred,
                                               sample_weight, sample_mask,
                                               self.learning_rate, k=k)
              else:
                  loss.update_terminal_regions(tree.tree_, X, y, residual, y_pred,
                                               sample_weight, sample_mask,
                                               self.learning_rate, k=k)
  
              # add tree to ensemble
              self.estimators_[i, k] = tree
  
          return y_pred
  
      def _check_params(self):
          """Check validity of parameters and raise ValueError if not valid. """
          if self.n_estimators <= 0:
              raise ValueError("n_estimators must be greater than 0 but "
                               "was %r" % self.n_estimators)
  
          if self.learning_rate <= 0.0:
              raise ValueError("learning_rate must be greater than 0 but "
                               "was %r" % self.learning_rate)
  
          if (self.loss not in self._SUPPORTED_LOSS
                  or self.loss not in LOSS_FUNCTIONS):
              raise ValueError("Loss '{0:s}' not supported. ".format(self.loss))
  
          if self.loss == 'deviance':
              loss_class = (MultinomialDeviance
                            if len(self.classes_) > 2
                            else BinomialDeviance)
          else:
              loss_class = LOSS_FUNCTIONS[self.loss]
  
          if self.loss in ('huber', 'quantile'):
              self.loss_ = loss_class(self.n_classes_, self.alpha)
          else:
              self.loss_ = loss_class(self.n_classes_)
  
          if not (0.0 < self.subsample <= 1.0):
              raise ValueError("subsample must be in (0,1] but "
                               "was %r" % self.subsample)
  
          if self.init is not None:
              if isinstance(self.init, six.string_types):
                  if self.init not in INIT_ESTIMATORS:
                      raise ValueError('init="%s" is not supported' % self.init)
              else:
                  if (not hasattr(self.init, 'fit')
                          or not hasattr(self.init, 'predict')):
                      raise ValueError("init=%r must be valid BaseEstimator "
                                       "and support both fit and "
                                       "predict" % self.init)
  
          if not (0.0 < self.alpha < 1.0):
              raise ValueError("alpha must be in (0.0, 1.0) but "
                               "was %r" % self.alpha)
  
          if isinstance(self.max_features, six.string_types):
              if self.max_features == "auto":
                  # if is_classification
                  if self.n_classes_ > 1:
                      max_features = max(1, int(np.sqrt(self.n_features_)))
                  else:
                      # is regression
                      max_features = self.n_features_
              elif self.max_features == "sqrt":
                  max_features = max(1, int(np.sqrt(self.n_features_)))
              elif self.max_features == "log2":
                  max_features = max(1, int(np.log2(self.n_features_)))
              else:
                  raise ValueError("Invalid value for max_features: %r. "
                                   "Allowed string values are 'auto', 'sqrt' "
                                   "or 'log2'." % self.max_features)
          elif self.max_features is None:
              max_features = self.n_features_
          elif isinstance(self.max_features, (numbers.Integral, np.integer)):
              max_features = self.max_features
          else:  # float
              if 0. < self.max_features <= 1.:
                  max_features = max(int(self.max_features *
                                         self.n_features_), 1)
              else:
                  raise ValueError("max_features must be in (0, n_features]")
  
          self.max_features_ = max_features
  
      def _init_state(self):
          """Initialize model state and allocate model state data structures. """
  
          if self.init is None:
              self.init_ = self.loss_.init_estimator()
          elif isinstance(self.init, six.string_types):
              self.init_ = INIT_ESTIMATORS[self.init]()
          else:
              self.init_ = self.init
  
          self.estimators_ = np.empty((self.n_estimators, self.loss_.K),
                                      dtype=np.object)
          self.train_score_ = np.zeros((self.n_estimators,), dtype=np.float64)
          # do oob?
          if self.subsample < 1.0:
              self.oob_improvement_ = np.zeros((self.n_estimators),
                                               dtype=np.float64)
  
      def _clear_state(self):
          """Clear the state of the gradient boosting model. """
          if hasattr(self, 'estimators_'):
              self.estimators_ = np.empty((0, 0), dtype=np.object)
          if hasattr(self, 'train_score_'):
              del self.train_score_
          if hasattr(self, 'oob_improvement_'):
              del self.oob_improvement_
          if hasattr(self, 'init_'):
              del self.init_
  
      def _resize_state(self):
          """Add additional ``n_estimators`` entries to all attributes. """
          # self.n_estimators is the number of additional est to fit
          total_n_estimators = self.n_estimators
          if total_n_estimators < self.estimators_.shape[0]:
              raise ValueError('resize with smaller n_estimators %d < %d' %
                               (total_n_estimators, self.estimators_[0]))
  
          self.estimators_.resize((total_n_estimators, self.loss_.K))
          self.train_score_.resize(total_n_estimators)
          if (self.subsample < 1 or hasattr(self, 'oob_improvement_')):
              # if do oob resize arrays or create new if not available
              if hasattr(self, 'oob_improvement_'):
                  self.oob_improvement_.resize(total_n_estimators)
              else:
                  self.oob_improvement_ = np.zeros((total_n_estimators,),
                                                   dtype=np.float64)
  
      def _is_initialized(self):
          return len(getattr(self, 'estimators_', [])) > 0
  
      def _check_initialized(self):
          """Check that the estimator is initialized, raising an error if not."""
          check_is_fitted(self, 'estimators_')
  
      @property
      @deprecated("Attribute n_features was deprecated in version 0.19 and "
                  "will be removed in 0.21.")
      def n_features(self):
          return self.n_features_
  
      def fit(self, X, y, sample_weight=None, monitor=None):
          """Fit the gradient boosting model.
  
          Parameters
          ----------
          X : array-like, shape = [n_samples, n_features]
              Training vectors, where n_samples is the number of samples
              and n_features is the number of features.
  
          y : array-like, shape = [n_samples]
              Target values (integers in classification, real numbers in
              regression)
              For classification, labels must correspond to classes.
  
          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.
  
          monitor : callable, optional
              The monitor is called after each iteration with the current
              iteration, a reference to the estimator and the local variables of
              ``_fit_stages`` as keyword arguments ``callable(i, self,
              locals())``. If the callable returns ``True`` the fitting procedure
              is stopped. The monitor can be used for various things such as
              computing held-out estimates, early stopping, model introspect, and
              snapshoting.
  
          Returns
          -------
          self : object
              Returns self.
          """
          # if not warmstart - clear the estimator state
          if not self.warm_start:
              self._clear_state()
  
          # Check input
          X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'], dtype=DTYPE)
          n_samples, self.n_features_ = X.shape
          if sample_weight is None:
              sample_weight = np.ones(n_samples, dtype=np.float32)
          else:
              sample_weight = column_or_1d(sample_weight, warn=True)
  
          check_consistent_length(X, y, sample_weight)
  
          y = self._validate_y(y)
  
          random_state = check_random_state(self.random_state)
          self._check_params()
  
          if not self._is_initialized():
              # init state
              self._init_state()
  
              # fit initial model - FIXME make sample_weight optional
              self.init_.fit(X, y, sample_weight)
  
              # init predictions
              y_pred = self.init_.predict(X)
              begin_at_stage = 0
          else:
              # add more estimators to fitted model
              # invariant: warm_start = True
              if self.n_estimators < self.estimators_.shape[0]:
                  raise ValueError('n_estimators=%d must be larger or equal to '
                                   'estimators_.shape[0]=%d when '
                                   'warm_start==True'
                                   % (self.n_estimators,
                                      self.estimators_.shape[0]))
              begin_at_stage = self.estimators_.shape[0]
              y_pred = self._decision_function(X)
              self._resize_state()
  
          X_idx_sorted = None
          presort = self.presort
          # Allow presort to be 'auto', which means True if the dataset is dense,
          # otherwise it will be False.
          if presort == 'auto' and issparse(X):
              presort = False
          elif presort == 'auto':
              presort = True
  
          if presort == True:
              if issparse(X):
                  raise ValueError("Presorting is not supported for sparse matrices.")
              else:
                  X_idx_sorted = np.asfortranarray(np.argsort(X, axis=0),
                                                   dtype=np.int32)
  
          # fit the boosting stages
          n_stages = self._fit_stages(X, y, y_pred, sample_weight, random_state,
                                      begin_at_stage, monitor, X_idx_sorted)
          # change shape of arrays after fit (early-stopping or additional ests)
          if n_stages != self.estimators_.shape[0]:
              self.estimators_ = self.estimators_[:n_stages]
              self.train_score_ = self.train_score_[:n_stages]
              if hasattr(self, 'oob_improvement_'):
                  self.oob_improvement_ = self.oob_improvement_[:n_stages]
  
          return self
  
      def _fit_stages(self, X, y, y_pred, sample_weight, random_state,
                      begin_at_stage=0, monitor=None, X_idx_sorted=None):
          """Iteratively fits the stages.
  
          For each stage it computes the progress (OOB, train score)
          and delegates to ``_fit_stage``.
          Returns the number of stages fit; might differ from ``n_estimators``
          due to early stopping.
          """
          n_samples = X.shape[0]
          do_oob = self.subsample < 1.0
          sample_mask = np.ones((n_samples, ), dtype=np.bool)
          n_inbag = max(1, int(self.subsample * n_samples))
          loss_ = self.loss_
  
          # Set min_weight_leaf from min_weight_fraction_leaf
          if self.min_weight_fraction_leaf != 0. and sample_weight is not None:
              min_weight_leaf = (self.min_weight_fraction_leaf *
                                 np.sum(sample_weight))
          else:
              min_weight_leaf = 0.
  
          if self.verbose:
              verbose_reporter = VerboseReporter(self.verbose)
              verbose_reporter.init(self, begin_at_stage)
  
          X_csc = csc_matrix(X) if issparse(X) else None
          X_csr = csr_matrix(X) if issparse(X) else None
  
          # perform boosting iterations
          i = begin_at_stage
          for i in range(begin_at_stage, self.n_estimators):
  
              # subsampling
              if do_oob:
                  sample_mask = _random_sample_mask(n_samples, n_inbag,
                                                    random_state)
                  # OOB score before adding this stage
                  old_oob_score = loss_(y[~sample_mask],
                                        y_pred[~sample_mask],
                                        sample_weight[~sample_mask])
  
              # fit next stage of trees
              y_pred = self._fit_stage(i, X, y, y_pred, sample_weight,
                                       sample_mask, random_state, X_idx_sorted,
                                       X_csc, X_csr)
  
              # track deviance (= loss)
              if do_oob:
                  self.train_score_[i] = loss_(y[sample_mask],
                                               y_pred[sample_mask],
                                               sample_weight[sample_mask])
                  self.oob_improvement_[i] = (
                      old_oob_score - loss_(y[~sample_mask],
                                            y_pred[~sample_mask],
                                            sample_weight[~sample_mask]))
              else:
                  # no need to fancy index w/ no subsampling
                  self.train_score_[i] = loss_(y, y_pred, sample_weight)
  
              if self.verbose > 0:
                  verbose_reporter.update(i, self)
  
              if monitor is not None:
                  early_stopping = monitor(i, self, locals())
                  if early_stopping:
                      break
          return i + 1
  
      def _make_estimator(self, append=True):
          # we don't need _make_estimator
          raise NotImplementedError()
  
      def _init_decision_function(self, X):
          """Check input and compute prediction of ``init``. """
          self._check_initialized()
          X = self.estimators_[0, 0]._validate_X_predict(X, check_input=True)
          if X.shape[1] != self.n_features_:
              raise ValueError("X.shape[1] should be {0:d}, not {1:d}.".format(
                  self.n_features_, X.shape[1]))
          score = self.init_.predict(X).astype(np.float64)
          return score
  
      def _decision_function(self, X):
          # for use in inner loop, not raveling the output in single-class case,
          # not doing input validation.
          score = self._init_decision_function(X)
          predict_stages(self.estimators_, X, self.learning_rate, score)
          return score
  
  
      def _staged_decision_function(self, X):
          """Compute decision function of ``X`` for each iteration.
  
          This method allows monitoring (i.e. determine error on testing set)
          after each stage.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          score : generator of array, shape = [n_samples, k]
              The decision function of the input samples. The order of the
              classes corresponds to that in the attribute `classes_`.
              Regression and binary classification are special cases with
              ``k == 1``, otherwise ``k==n_classes``.
          """
          X = check_array(X, dtype=DTYPE, order="C",  accept_sparse='csr')
          score = self._init_decision_function(X)
          for i in range(self.estimators_.shape[0]):
              predict_stage(self.estimators_, i, X, self.learning_rate, score)
              yield score.copy()
  
      @property
      def feature_importances_(self):
          """Return the feature importances (the higher, the more important the
             feature).
  
          Returns
          -------
          feature_importances_ : array, shape = [n_features]
          """
          self._check_initialized()
  
          total_sum = np.zeros((self.n_features_, ), dtype=np.float64)
          for stage in self.estimators_:
              stage_sum = sum(tree.feature_importances_
                              for tree in stage) / len(stage)
              total_sum += stage_sum
  
          importances = total_sum / len(self.estimators_)
          return importances
  
      def _validate_y(self, y):
          self.n_classes_ = 1
          if y.dtype.kind == 'O':
              y = y.astype(np.float64)
          # Default implementation
          return y
  
      def apply(self, X):
          """Apply trees in the ensemble to X, return leaf indices.
  
          .. versionadded:: 0.17
  
          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 to a sparse ``csr_matrix``.
  
          Returns
          -------
          X_leaves : array_like, shape = [n_samples, n_estimators, n_classes]
              For each datapoint x in X and for each tree in the ensemble,
              return the index of the leaf x ends up in each estimator.
              In the case of binary classification n_classes is 1.
          """
  
          self._check_initialized()
          X = self.estimators_[0, 0]._validate_X_predict(X, check_input=True)
  
          # n_classes will be equal to 1 in the binary classification or the
          # regression case.
          n_estimators, n_classes = self.estimators_.shape
          leaves = np.zeros((X.shape[0], n_estimators, n_classes))
  
          for i in range(n_estimators):
              for j in range(n_classes):
                  estimator = self.estimators_[i, j]
                  leaves[:, i, j] = estimator.apply(X, check_input=False)
  
          return leaves
  
  
  class GradientBoostingClassifier(BaseGradientBoosting, ClassifierMixin):
      """Gradient Boosting for classification.
  
      GB builds an additive model in a
      forward stage-wise fashion; it allows for the optimization of
      arbitrary differentiable loss functions. In each stage ``n_classes_``
      regression trees are fit on the negative gradient of the
      binomial or multinomial deviance loss function. Binary classification
      is a special case where only a single regression tree is induced.
  
      Read more in the :ref:`User Guide <gradient_boosting>`.
  
      Parameters
      ----------
      loss : {'deviance', 'exponential'}, optional (default='deviance')
          loss function to be optimized. 'deviance' refers to
          deviance (= logistic regression) for classification
          with probabilistic outputs. For loss 'exponential' gradient
          boosting recovers the AdaBoost algorithm.
  
      learning_rate : float, optional (default=0.1)
          learning rate shrinks the contribution of each tree by `learning_rate`.
          There is a trade-off between learning_rate and n_estimators.
  
      n_estimators : int (default=100)
          The number of boosting stages to perform. Gradient boosting
          is fairly robust to over-fitting so a large number usually
          results in better performance.
  
      max_depth : integer, optional (default=3)
          maximum depth of the individual regression estimators. The maximum
          depth limits the number of nodes in the tree. Tune this parameter
          for best performance; the best value depends on the interaction
          of the input variables.
  
      criterion : string, optional (default="friedman_mse")
          The function to measure the quality of a split. Supported criteria
          are "friedman_mse" for the mean squared error with improvement
          score by Friedman, "mse" for mean squared error, and "mae" for
          the mean absolute error. The default value of "friedman_mse" is
          generally the best as it can provide a better approximation in
          some cases.
  
          .. versionadded:: 0.18
  
      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.
  
      subsample : float, optional (default=1.0)
          The fraction of samples to be used for fitting the individual base
          learners. If smaller than 1.0 this results in Stochastic Gradient
          Boosting. `subsample` interacts with the parameter `n_estimators`.
          Choosing `subsample < 1.0` leads to a reduction of variance
          and an increase in bias.
  
      max_features : int, float, string or None, optional (default=None)
          The number of features to consider when looking for the best split:
  
          - If int, then consider `max_features` features at each split.
          - If float, then `max_features` is a 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`.
  
          Choosing `max_features < n_features` leads to a reduction of variance
          and an increase in bias.
  
          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_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
  
      init : BaseEstimator, None, optional (default=None)
          An estimator object that is used to compute the initial
          predictions. ``init`` has to provide ``fit`` and ``predict``.
          If None it uses ``loss.init_estimator``.
  
      verbose : int, default: 0
          Enable verbose output. If 1 then it prints progress and performance
          once in a while (the more trees the lower the frequency). If greater
          than 1 then it prints progress and performance for every tree.
  
      warm_start : bool, default: False
          When set to ``True``, reuse the solution of the previous call to fit
          and add more estimators to the ensemble, otherwise, just erase the
          previous solution.
  
      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`.
  
      presort : bool or 'auto', optional (default='auto')
          Whether to presort the data to speed up the finding of best splits in
          fitting. Auto mode by default will use presorting on dense data and
          default to normal sorting on sparse data. Setting presort to true on
          sparse data will raise an error.
  
          .. versionadded:: 0.17
             *presort* parameter.
  
      Attributes
      ----------
      feature_importances_ : array, shape = [n_features]
          The feature importances (the higher, the more important the feature).
  
      oob_improvement_ : array, shape = [n_estimators]
          The improvement in loss (= deviance) on the out-of-bag samples
          relative to the previous iteration.
          ``oob_improvement_[0]`` is the improvement in
          loss of the first stage over the ``init`` estimator.
  
      train_score_ : array, shape = [n_estimators]
          The i-th score ``train_score_[i]`` is the deviance (= loss) of the
          model at iteration ``i`` on the in-bag sample.
          If ``subsample == 1`` this is the deviance on the training data.
  
      loss_ : LossFunction
          The concrete ``LossFunction`` object.
  
      init : BaseEstimator
          The estimator that provides the initial predictions.
          Set via the ``init`` argument or ``loss.init_estimator``.
  
      estimators_ : ndarray of DecisionTreeRegressor, shape = [n_estimators, ``loss_.K``]
          The collection of fitted sub-estimators. ``loss_.K`` is 1 for binary
          classification, otherwise n_classes.
  
  
      See also
      --------
      sklearn.tree.DecisionTreeClassifier, RandomForestClassifier
      AdaBoostClassifier
  
      References
      ----------
      J. Friedman, Greedy Function Approximation: A Gradient Boosting
      Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.
  
      J. Friedman, Stochastic Gradient Boosting, 1999
  
      T. Hastie, R. Tibshirani and J. Friedman.
      Elements of Statistical Learning Ed. 2, Springer, 2009.
      """
  
      _SUPPORTED_LOSS = ('deviance', 'exponential')
  
      def __init__(self, loss='deviance', learning_rate=0.1, n_estimators=100,
                   subsample=1.0, criterion='friedman_mse', min_samples_split=2,
                   min_samples_leaf=1, min_weight_fraction_leaf=0.,
                   max_depth=3, min_impurity_split=1e-7, init=None,
                   random_state=None, max_features=None, verbose=0,
                   max_leaf_nodes=None, warm_start=False,
                   presort='auto'):
  
          super(GradientBoostingClassifier, self).__init__(
              loss=loss, learning_rate=learning_rate, n_estimators=n_estimators,
              criterion=criterion, min_samples_split=min_samples_split,
              min_samples_leaf=min_samples_leaf,
              min_weight_fraction_leaf=min_weight_fraction_leaf,
              max_depth=max_depth, init=init, subsample=subsample,
              max_features=max_features,
              random_state=random_state, verbose=verbose,
              max_leaf_nodes=max_leaf_nodes,
              min_impurity_split=min_impurity_split,
              warm_start=warm_start,
              presort=presort)
  
      def _validate_y(self, y):
          check_classification_targets(y)
          self.classes_, y = np.unique(y, return_inverse=True)
          self.n_classes_ = len(self.classes_)
          return y
  
      def decision_function(self, X):
          """Compute the decision function of ``X``.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          score : array, shape = [n_samples, n_classes] or [n_samples]
              The decision function of the input samples. The order of the
              classes corresponds to that in the attribute `classes_`.
              Regression and binary classification produce an array of shape
              [n_samples].
          """
          X = check_array(X, dtype=DTYPE, order="C",  accept_sparse='csr')
          score = self._decision_function(X)
          if score.shape[1] == 1:
              return score.ravel()
          return score
  
      def staged_decision_function(self, X):
          """Compute decision function of ``X`` for each iteration.
  
          This method allows monitoring (i.e. determine error on testing set)
          after each stage.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          score : generator of array, shape = [n_samples, k]
              The decision function of the input samples. The order of the
              classes corresponds to that in the attribute `classes_`.
              Regression and binary classification are special cases with
              ``k == 1``, otherwise ``k==n_classes``.
          """
          for dec in self._staged_decision_function(X):
              # no yield from in Python2.X
              yield dec
  
      def predict(self, X):
          """Predict class for X.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          y : array of shape = ["n_samples]
              The predicted values.
          """
          score = self.decision_function(X)
          decisions = self.loss_._score_to_decision(score)
          return self.classes_.take(decisions, axis=0)
  
      def staged_predict(self, X):
          """Predict class at each stage for X.
  
          This method allows monitoring (i.e. determine error on testing set)
          after each stage.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          y : generator of array of shape = [n_samples]
              The predicted value of the input samples.
          """
          for score in self._staged_decision_function(X):
              decisions = self.loss_._score_to_decision(score)
              yield self.classes_.take(decisions, axis=0)
  
      def predict_proba(self, X):
          """Predict class probabilities for X.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Raises
          ------
          AttributeError
              If the ``loss`` does not support probabilities.
  
          Returns
          -------
          p : array of shape = [n_samples]
              The class probabilities of the input samples. The order of the
              classes corresponds to that in the attribute `classes_`.
          """
          score = self.decision_function(X)
          try:
              return self.loss_._score_to_proba(score)
          except NotFittedError:
              raise
          except AttributeError:
              raise AttributeError('loss=%r does not support predict_proba' %
                                   self.loss)
  
      def predict_log_proba(self, X):
          """Predict class log-probabilities for X.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Raises
          ------
          AttributeError
              If the ``loss`` does not support probabilities.
  
          Returns
          -------
          p : array of shape = [n_samples]
              The class log-probabilities of the input samples. The order of the
              classes corresponds to that in the attribute `classes_`.
          """
          proba = self.predict_proba(X)
          return np.log(proba)
  
      def staged_predict_proba(self, X):
          """Predict class probabilities at each stage for X.
  
          This method allows monitoring (i.e. determine error on testing set)
          after each stage.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          y : generator of array of shape = [n_samples]
              The predicted value of the input samples.
          """
          try:
              for score in self._staged_decision_function(X):
                  yield self.loss_._score_to_proba(score)
          except NotFittedError:
              raise
          except AttributeError:
              raise AttributeError('loss=%r does not support predict_proba' %
                                   self.loss)
  
  
  class GradientBoostingRegressor(BaseGradientBoosting, RegressorMixin):
      """Gradient Boosting for regression.
  
      GB builds an additive model in a forward stage-wise fashion;
      it allows for the optimization of arbitrary differentiable loss functions.
      In each stage a regression tree is fit on the negative gradient of the
      given loss function.
  
      Read more in the :ref:`User Guide <gradient_boosting>`.
  
      Parameters
      ----------
      loss : {'ls', 'lad', 'huber', 'quantile'}, optional (default='ls')
          loss function to be optimized. 'ls' refers to least squares
          regression. 'lad' (least absolute deviation) is a highly robust
          loss function solely based on order information of the input
          variables. 'huber' is a combination of the two. 'quantile'
          allows quantile regression (use `alpha` to specify the quantile).
  
      learning_rate : float, optional (default=0.1)
          learning rate shrinks the contribution of each tree by `learning_rate`.
          There is a trade-off between learning_rate and n_estimators.
  
      n_estimators : int (default=100)
          The number of boosting stages to perform. Gradient boosting
          is fairly robust to over-fitting so a large number usually
          results in better performance.
  
      max_depth : integer, optional (default=3)
          maximum depth of the individual regression estimators. The maximum
          depth limits the number of nodes in the tree. Tune this parameter
          for best performance; the best value depends on the interaction
          of the input variables.
  
      criterion : string, optional (default="friedman_mse")
          The function to measure the quality of a split. Supported criteria
          are "friedman_mse" for the mean squared error with improvement
          score by Friedman, "mse" for mean squared error, and "mae" for
          the mean absolute error. The default value of "friedman_mse" is
          generally the best as it can provide a better approximation in
          some cases.
  
          .. versionadded:: 0.18
  
      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.
  
      subsample : float, optional (default=1.0)
          The fraction of samples to be used for fitting the individual base
          learners. If smaller than 1.0 this results in Stochastic Gradient
          Boosting. `subsample` interacts with the parameter `n_estimators`.
          Choosing `subsample < 1.0` leads to a reduction of variance
          and an increase in bias.
  
      max_features : int, float, string or None, optional (default=None)
          The number of features to consider when looking for the best split:
  
          - If int, then consider `max_features` features at each split.
          - If float, then `max_features` is a 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`.
  
          Choosing `max_features < n_features` leads to a reduction of variance
          and an increase in bias.
  
          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_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
  
      alpha : float (default=0.9)
          The alpha-quantile of the huber loss function and the quantile
          loss function. Only if ``loss='huber'`` or ``loss='quantile'``.
  
      init : BaseEstimator, None, optional (default=None)
          An estimator object that is used to compute the initial
          predictions. ``init`` has to provide ``fit`` and ``predict``.
          If None it uses ``loss.init_estimator``.
  
      verbose : int, default: 0
          Enable verbose output. If 1 then it prints progress and performance
          once in a while (the more trees the lower the frequency). If greater
          than 1 then it prints progress and performance for every tree.
  
      warm_start : bool, default: False
          When set to ``True``, reuse the solution of the previous call to fit
          and add more estimators to the ensemble, otherwise, just erase the
          previous solution.
  
      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`.
  
      presort : bool or 'auto', optional (default='auto')
          Whether to presort the data to speed up the finding of best splits in
          fitting. Auto mode by default will use presorting on dense data and
          default to normal sorting on sparse data. Setting presort to true on
          sparse data will raise an error.
  
          .. versionadded:: 0.17
             optional parameter *presort*.
  
      Attributes
      ----------
      feature_importances_ : array, shape = [n_features]
          The feature importances (the higher, the more important the feature).
  
      oob_improvement_ : array, shape = [n_estimators]
          The improvement in loss (= deviance) on the out-of-bag samples
          relative to the previous iteration.
          ``oob_improvement_[0]`` is the improvement in
          loss of the first stage over the ``init`` estimator.
  
      train_score_ : array, shape = [n_estimators]
          The i-th score ``train_score_[i]`` is the deviance (= loss) of the
          model at iteration ``i`` on the in-bag sample.
          If ``subsample == 1`` this is the deviance on the training data.
  
      loss_ : LossFunction
          The concrete ``LossFunction`` object.
  
      `init` : BaseEstimator
          The estimator that provides the initial predictions.
          Set via the ``init`` argument or ``loss.init_estimator``.
  
      estimators_ : ndarray of DecisionTreeRegressor, shape = [n_estimators, 1]
          The collection of fitted sub-estimators.
  
      See also
      --------
      DecisionTreeRegressor, RandomForestRegressor
  
      References
      ----------
      J. Friedman, Greedy Function Approximation: A Gradient Boosting
      Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.
  
      J. Friedman, Stochastic Gradient Boosting, 1999
  
      T. Hastie, R. Tibshirani and J. Friedman.
      Elements of Statistical Learning Ed. 2, Springer, 2009.
      """
  
      _SUPPORTED_LOSS = ('ls', 'lad', 'huber', 'quantile')
  
      def __init__(self, loss='ls', learning_rate=0.1, n_estimators=100,
                   subsample=1.0, criterion='friedman_mse', min_samples_split=2,
                   min_samples_leaf=1, min_weight_fraction_leaf=0.,
                   max_depth=3, min_impurity_split=1e-7, init=None, random_state=None,
                   max_features=None, alpha=0.9, verbose=0, max_leaf_nodes=None,
                   warm_start=False, presort='auto'):
  
          super(GradientBoostingRegressor, self).__init__(
              loss=loss, learning_rate=learning_rate, n_estimators=n_estimators,
              criterion=criterion, min_samples_split=min_samples_split,
              min_samples_leaf=min_samples_leaf,
              min_weight_fraction_leaf=min_weight_fraction_leaf,
              max_depth=max_depth, init=init, subsample=subsample,
              max_features=max_features, min_impurity_split=min_impurity_split,
              random_state=random_state, alpha=alpha, verbose=verbose,
              max_leaf_nodes=max_leaf_nodes, warm_start=warm_start,
              presort=presort)
  
      def predict(self, X):
          """Predict regression target for X.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          y : array of shape = [n_samples]
              The predicted values.
          """
          X = check_array(X, dtype=DTYPE, order="C",  accept_sparse='csr')
          return self._decision_function(X).ravel()
  
      def staged_predict(self, X):
          """Predict regression target at each stage for X.
  
          This method allows monitoring (i.e. determine error on testing set)
          after each stage.
  
          Parameters
          ----------
          X : array-like or sparse matrix, shape = [n_samples, n_features]
              The input samples. Internally, it will be converted to
              ``dtype=np.float32`` and if a sparse matrix is provided
              to a sparse ``csr_matrix``.
  
          Returns
          -------
          y : generator of array of shape = [n_samples]
              The predicted value of the input samples.
          """
          for y in self._staged_decision_function(X):
              yield y.ravel()
  
      def apply(self, X):
          """Apply trees in the ensemble to X, return leaf indices.
  
          .. versionadded:: 0.17
  
          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 to 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 ensemble,
              return the index of the leaf x ends up in each estimator.
          """
  
          leaves = super(GradientBoostingRegressor, self).apply(X)
          leaves = leaves.reshape(X.shape[0], self.estimators_.shape[0])
          return leaves
  