"""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


"""
=======================================================================
Shrinkage covariance estimation: LedoitWolf vs OAS and max-likelihood
=======================================================================

When working with covariance estimation, the usual approach is to use
a maximum likelihood estimator, such as the
:class:`sklearn.covariance.EmpiricalCovariance`. It is unbiased, i.e. it
converges to the true (population) covariance when given many
observations. However, it can also be beneficial to regularize it, in
order to reduce its variance; this, in turn, introduces some bias. This
example illustrates the simple regularization used in
:ref:`shrunk_covariance` estimators. In particular, it focuses on how to
set the amount of regularization, i.e. how to choose the bias-variance
trade-off.

Here we compare 3 approaches:

* Setting the parameter by cross-validating the likelihood on three folds
  according to a grid of potential shrinkage parameters.

* A close formula proposed by Ledoit and Wolf to compute
  the asymptotically optimal regularization parameter (minimizing a MSE
  criterion), yielding the :class:`sklearn.covariance.LedoitWolf`
  covariance estimate.

* An improvement of the Ledoit-Wolf shrinkage, the
  :class:`sklearn.covariance.OAS`, proposed by Chen et al. Its
  convergence is significantly better under the assumption that the data
  are Gaussian, in particular for small samples.

To quantify estimation error, we plot the likelihood of unseen data for
different values of the shrinkage parameter. We also show the choices by
cross-validation, or with the LedoitWolf and OAS estimates.

Note that the maximum likelihood estimate corresponds to no shrinkage,
and thus performs poorly. The Ledoit-Wolf estimate performs really well,
as it is close to the optimal and is computational not costly. In this
example, the OAS estimate is a bit further away. Interestingly, both
approaches outperform cross-validation, which is significantly most
computationally costly.

"""
print(__doc__)

import numpy as np
import matplotlib.pyplot as plt
from scipy import linalg

from sklearn.covariance import LedoitWolf, OAS, ShrunkCovariance, \
    log_likelihood, empirical_covariance
from sklearn.grid_search import GridSearchCV

###############################################################################
# Generate sample data
n_features, n_samples = 40, 20
np.random.seed(42)
base_X_train = np.random.normal(size=(n_samples, n_features))
base_X_test = np.random.normal(size=(n_samples, n_features))

# Color samples
coloring_matrix = np.random.normal(size=(n_features, n_features))
X_train = np.dot(base_X_train, coloring_matrix)
X_test = np.dot(base_X_test, coloring_matrix)

###############################################################################
# Compute the likelihood on test data

# spanning a range of possible shrinkage coefficient values
shrinkages = np.logspace(-2, 0, 30)
negative_logliks = [-ShrunkCovariance(shrinkage=s).fit(X_train).score(X_test)
                    for s in shrinkages]

# under the ground-truth model, which we would not have access to in real
# settings
real_cov = np.dot(coloring_matrix.T, coloring_matrix)
emp_cov = empirical_covariance(X_train)
loglik_real = -log_likelihood(emp_cov, linalg.inv(real_cov))

###############################################################################
# Compare different approaches to setting the parameter

# GridSearch for an optimal shrinkage coefficient
tuned_parameters = [{'shrinkage': shrinkages}]
cv = GridSearchCV(ShrunkCovariance(), tuned_parameters)
cv.fit(X_train)

# Ledoit-Wolf optimal shrinkage coefficient estimate
lw = LedoitWolf()
loglik_lw = lw.fit(X_train).score(X_test)

# OAS coefficient estimate
oa = OAS()
loglik_oa = oa.fit(X_train).score(X_test)

###############################################################################
# Plot results
fig = plt.figure()
plt.title("Regularized covariance: likelihood and shrinkage coefficient")
plt.xlabel('Regularizaton parameter: shrinkage coefficient')
plt.ylabel('Error: negative log-likelihood on test data')
# range shrinkage curve
plt.loglog(shrinkages, negative_logliks, label="Negative log-likelihood")

plt.plot(plt.xlim(), 2 * [loglik_real], '--r',
         label="Real covariance likelihood")

# adjust view
lik_max = np.amax(negative_logliks)
lik_min = np.amin(negative_logliks)
ymin = lik_min - 6. * np.log((plt.ylim()[1] - plt.ylim()[0]))
ymax = lik_max + 10. * np.log(lik_max - lik_min)
xmin = shrinkages[0]
xmax = shrinkages[-1]
# LW likelihood
plt.vlines(lw.shrinkage_, ymin, -loglik_lw, color='magenta',
           linewidth=3, label='Ledoit-Wolf estimate')
# OAS likelihood
plt.vlines(oa.shrinkage_, ymin, -loglik_oa, color='purple',
           linewidth=3, label='OAS estimate')
# best CV estimator likelihood
plt.vlines(cv.best_estimator_.shrinkage, ymin,
           -cv.best_estimator_.score(X_test), color='cyan',
           linewidth=3, label='Cross-validation best estimate')

plt.ylim(ymin, ymax)
plt.xlim(xmin, xmax)
plt.legend()

plt.show()


import unittest
import copy
import sys

from nose.tools import assert_true
import numpy as np
from numpy.testing import (assert_array_equal, assert_array_almost_equal,
                           assert_raises)
from scipy import stats
from sklearn import mixture
from sklearn.datasets.samples_generator import make_spd_matrix
from sklearn.utils.testing import assert_greater
from sklearn.utils.testing import assert_raise_message
from sklearn.metrics.cluster import adjusted_rand_score
from sklearn.externals.six.moves import cStringIO as StringIO

rng = np.random.RandomState(0)

def test_sample_gaussian():
    # Test sample generation from mixture.sample_gaussian where covariance
    # is diagonal, spherical and full

    n_features, n_samples = 2, 300
    axis = 1
    mu = rng.randint(10) * rng.rand(n_features)
    cv = (rng.rand(n_features) + 1.0) ** 2

    samples = mixture.sample_gaussian(
        mu, cv, covariance_type='diag', n_samples=n_samples)

    assert_true(np.allclose(samples.mean(axis), mu, atol=1.3))
    assert_true(np.allclose(samples.var(axis), cv, atol=1.5))

    # the same for spherical covariances
    cv = (rng.rand() + 1.0) ** 2
    samples = mixture.sample_gaussian(
        mu, cv, covariance_type='spherical', n_samples=n_samples)

    assert_true(np.allclose(samples.mean(axis), mu, atol=1.5))
    assert_true(np.allclose(
        samples.var(axis), np.repeat(cv, n_features), atol=1.5))

    # and for full covariances
    A = rng.randn(n_features, n_features)
    cv = np.dot(A.T, A) + np.eye(n_features)
    samples = mixture.sample_gaussian(
        mu, cv, covariance_type='full', n_samples=n_samples)
    assert_true(np.allclose(samples.mean(axis), mu, atol=1.3))
    assert_true(np.allclose(np.cov(samples), cv, atol=2.5))

    # Numerical stability check: in SciPy 0.12.0 at least, eigh may return
    # tiny negative values in its second return value.
    from sklearn.mixture import sample_gaussian
    x = sample_gaussian([0, 0], [[4, 3], [1, .1]],
                        covariance_type='full', random_state=42)
    print(x)
    assert_true(np.isfinite(x).all())

def _naive_lmvnpdf_diag(X, mu, cv):
    # slow and naive implementation of lmvnpdf
    ref = np.empty((len(X), len(mu)))
    stds = np.sqrt(cv)
    for i, (m, std) in enumerate(zip(mu, stds)):
        ref[:, i] = np.log(stats.norm.pdf(X, m, std)).sum(axis=1)
    return ref

def test_lmvnpdf_diag():
    # test a slow and naive implementation of lmvnpdf and
    # compare it to the vectorized version (mixture.lmvnpdf) to test
    # for correctness
    n_features, n_components, n_samples = 2, 3, 10
    mu = rng.randint(10) * rng.rand(n_components, n_features)
    cv = (rng.rand(n_components, n_features) + 1.0) ** 2
    X = rng.randint(10) * rng.rand(n_samples, n_features)

    ref = _naive_lmvnpdf_diag(X, mu, cv)
    lpr = mixture.log_multivariate_normal_density(X, mu, cv, 'diag')
    assert_array_almost_equal(lpr, ref)

def test_lmvnpdf_spherical():
    n_features, n_components, n_samples = 2, 3, 10

    mu = rng.randint(10) * rng.rand(n_components, n_features)
    spherecv = rng.rand(n_components, 1) ** 2 + 1
    X = rng.randint(10) * rng.rand(n_samples, n_features)

    cv = np.tile(spherecv, (n_features, 1))
    reference = _naive_lmvnpdf_diag(X, mu, cv)
    lpr = mixture.log_multivariate_normal_density(X, mu, spherecv,
                                                  'spherical')
    assert_array_almost_equal(lpr, reference)

def test_lmvnpdf_full():
    n_features, n_components, n_samples = 2, 3, 10

    mu = rng.randint(10) * rng.rand(n_components, n_features)
    cv = (rng.rand(n_components, n_features) + 1.0) ** 2
    X = rng.randint(10) * rng.rand(n_samples, n_features)

    fullcv = np.array([np.diag(x) for x in cv])

    reference = _naive_lmvnpdf_diag(X, mu, cv)
    lpr = mixture.log_multivariate_normal_density(X, mu, fullcv, 'full')
    assert_array_almost_equal(lpr, reference)

def test_lvmpdf_full_cv_non_positive_definite():
    n_features, n_samples = 2, 10
    rng = np.random.RandomState(0)
    X = rng.randint(10) * rng.rand(n_samples, n_features)
    mu = np.mean(X, 0)
    cv = np.array([[[-1, 0], [0, 1]]])
    expected_message = "'covars' must be symmetric, positive-definite"
    assert_raise_message(ValueError, expected_message,
                         mixture.log_multivariate_normal_density,
                         X, mu, cv, 'full')

def test_GMM_attributes():
    n_components, n_features = 10, 4
    covariance_type = 'diag'
    g = mixture.GMM(n_components, covariance_type, random_state=rng)
    weights = rng.rand(n_components)
    weights = weights / weights.sum()
    means = rng.randint(-20, 20, (n_components, n_features))

    assert_true(g.n_components == n_components)
    assert_true(g.covariance_type == covariance_type)

    g.weights_ = weights
    assert_array_almost_equal(g.weights_, weights)
    g.means_ = means
    assert_array_almost_equal(g.means_, means)

    covars = (0.1 + 2 * rng.rand(n_components, n_features)) ** 2
    g.covars_ = covars
    assert_array_almost_equal(g.covars_, covars)
    assert_raises(ValueError, g._set_covars, [])
    assert_raises(ValueError, g._set_covars,
                  np.zeros((n_components - 2, n_features)))

    assert_raises(ValueError, mixture.GMM, n_components=20,
                  covariance_type='badcovariance_type')

class GMMTester():
    do_test_eval = True

    def _setUp(self):
        self.n_components = 10
        self.n_features = 4
        self.weights = rng.rand(self.n_components)
        self.weights = self.weights / self.weights.sum()
        self.means = rng.randint(-20, 20, (self.n_components, self.n_features))
        self.threshold = -0.5
        self.I = np.eye(self.n_features)
        self.covars = {
            'spherical': (0.1 + 2 * rng.rand(self.n_components,
                                             self.n_features)) ** 2,
            'tied': (make_spd_matrix(self.n_features, random_state=0)
                     + 5 * self.I),
            'diag': (0.1 + 2 * rng.rand(self.n_components,
                                        self.n_features)) ** 2,
            'full': np.array([make_spd_matrix(self.n_features, random_state=0)
                              + 5 * self.I for x in range(self.n_components)])}

    def test_eval(self):
        if not self.do_test_eval:
            return  # DPGMM does not support setting the means and
        # covariances before fitting There is no way of fixing this
        # due to the variational parameters being more expressive than
        # covariance matrices
        g = self.model(n_components=self.n_components,
                       covariance_type=self.covariance_type, random_state=rng)
        # Make sure the means are far apart so responsibilities.argmax()
        # picks the actual component used to generate the observations.
        g.means_ = 20 * self.means
        g.covars_ = self.covars[self.covariance_type]
        g.weights_ = self.weights

        gaussidx = np.repeat(np.arange(self.n_components), 5)
        n_samples = len(gaussidx)
        X = rng.randn(n_samples, self.n_features) + g.means_[gaussidx]

        ll, responsibilities = g.score_samples(X)

        self.assertEqual(len(ll), n_samples)
        self.assertEqual(responsibilities.shape,
                         (n_samples, self.n_components))
        assert_array_almost_equal(responsibilities.sum(axis=1),
                                  np.ones(n_samples))
        assert_array_equal(responsibilities.argmax(axis=1), gaussidx)

    def test_sample(self, n=100):
        g = self.model(n_components=self.n_components,
                       covariance_type=self.covariance_type, random_state=rng)
        # Make sure the means are far apart so responsibilities.argmax()
        # picks the actual component used to generate the observations.
        g.means_ = 20 * self.means
        g.covars_ = np.maximum(self.covars[self.covariance_type], 0.1)
        g.weights_ = self.weights

        samples = g.sample(n)
        self.assertEqual(samples.shape, (n, self.n_features))

    def test_train(self, params='wmc'):
        g = mixture.GMM(n_components=self.n_components,
                        covariance_type=self.covariance_type)
        g.weights_ = self.weights
        g.means_ = self.means
        g.covars_ = 20 * self.covars[self.covariance_type]

        # Create a training set by sampling from the predefined distribution.
        X = g.sample(n_samples=100)
        g = self.model(n_components=self.n_components,
                       covariance_type=self.covariance_type,
                       random_state=rng, min_covar=1e-1,
                       n_iter=1, init_params=params)
        g.fit(X)

        # Do one training iteration at a time so we can keep track of
        # the log likelihood to make sure that it increases after each
        # iteration.
        trainll = []
        for _ in range(5):
            g.params = params
            g.init_params = ''
            g.fit(X)
            trainll.append(self.score(g, X))
        g.n_iter = 10
        g.init_params = ''
        g.params = params
        g.fit(X)  # finish fitting

        # Note that the log likelihood will sometimes decrease by a
        # very small amount after it has more or less converged due to
        # the addition of min_covar to the covariance (to prevent
        # underflow).  This is why the threshold is set to -0.5
        # instead of 0.
        delta_min = np.diff(trainll).min()
        self.assertTrue(
            delta_min > self.threshold,
            "The min nll increase is %f which is lower than the admissible"
            " threshold of %f, for model %s. The likelihoods are %s."
            % (delta_min, self.threshold, self.covariance_type, trainll))

    def test_train_degenerate(self, params='wmc'):
        # Train on degenerate data with 0 in some dimensions
        # Create a training set by sampling from the predefined distribution.
        X = rng.randn(100, self.n_features)
        X.T[1:] = 0
        g = self.model(n_components=2, covariance_type=self.covariance_type,
                       random_state=rng, min_covar=1e-3, n_iter=5,
                       init_params=params)
        g.fit(X)
        trainll = g.score(X)
        self.assertTrue(np.sum(np.abs(trainll / 100 / X.shape[1])) < 5)

    def test_train_1d(self, params='wmc'):
        # Train on 1-D data
        # Create a training set by sampling from the predefined distribution.
        X = rng.randn(100, 1)
        # X.T[1:] = 0
        g = self.model(n_components=2, covariance_type=self.covariance_type,
                       random_state=rng, min_covar=1e-7, n_iter=5,
                       init_params=params)
        g.fit(X)
        trainll = g.score(X)
        if isinstance(g, mixture.DPGMM):
            self.assertTrue(np.sum(np.abs(trainll / 100)) < 5)
        else:
            self.assertTrue(np.sum(np.abs(trainll / 100)) < 2)

    def score(self, g, X):
        return g.score(X).sum()

class TestGMMWithSphericalCovars(unittest.TestCase, GMMTester):
    covariance_type = 'spherical'
    model = mixture.GMM
    setUp = GMMTester._setUp

class TestGMMWithDiagonalCovars(unittest.TestCase, GMMTester):
    covariance_type = 'diag'
    model = mixture.GMM
    setUp = GMMTester._setUp

class TestGMMWithTiedCovars(unittest.TestCase, GMMTester):
    covariance_type = 'tied'
    model = mixture.GMM
    setUp = GMMTester._setUp

class TestGMMWithFullCovars(unittest.TestCase, GMMTester):
    covariance_type = 'full'
    model = mixture.GMM
    setUp = GMMTester._setUp

def test_multiple_init():
    # Test that multiple inits does not much worse than a single one
    X = rng.randn(30, 5)
    X[:10] += 2
    g = mixture.GMM(n_components=2, covariance_type='spherical',
                    random_state=rng, min_covar=1e-7, n_iter=5)
    train1 = g.fit(X).score(X).sum()
    g.n_init = 5
    train2 = g.fit(X).score(X).sum()
    assert_true(train2 >= train1 - 1.e-2)

def test_n_parameters():
    # Test that the right number of parameters is estimated
    n_samples, n_dim, n_components = 7, 5, 2
    X = rng.randn(n_samples, n_dim)
    n_params = {'spherical': 13, 'diag': 21, 'tied': 26, 'full': 41}
    for cv_type in ['full', 'tied', 'diag', 'spherical']:
        g = mixture.GMM(n_components=n_components, covariance_type=cv_type,
                        random_state=rng, min_covar=1e-7, n_iter=1)
        g.fit(X)
        assert_true(g._n_parameters() == n_params[cv_type])

def test_1d_1component():
    # Test all of the covariance_types return the same BIC score for
    # 1-dimensional, 1 component fits.
    n_samples, n_dim, n_components = 100, 1, 1
    X = rng.randn(n_samples, n_dim)
    g_full = mixture.GMM(n_components=n_components, covariance_type='full',
                         random_state=rng, min_covar=1e-7, n_iter=1)
    g_full.fit(X)
    g_full_bic = g_full.bic(X)
    for cv_type in ['tied', 'diag', 'spherical']:
        g = mixture.GMM(n_components=n_components, covariance_type=cv_type,
                        random_state=rng, min_covar=1e-7, n_iter=1)
        g.fit(X)
        assert_array_almost_equal(g.bic(X), g_full_bic)

def assert_fit_predict_correct(model, X):
    model2 = copy.deepcopy(model)

    predictions_1 = model.fit(X).predict(X)
    predictions_2 = model2.fit_predict(X)

    assert adjusted_rand_score(predictions_1, predictions_2) == 1.0

def test_fit_predict():
    """
    test that gmm.fit_predict is equivalent to gmm.fit + gmm.predict
    """
    lrng = np.random.RandomState(101)

    n_samples, n_dim, n_comps = 100, 2, 2
    mu = np.array([[8, 8]])
    component_0 = lrng.randn(n_samples, n_dim)
    component_1 = lrng.randn(n_samples, n_dim) + mu
    X = np.vstack((component_0, component_1))

    for m_constructor in (mixture.GMM, mixture.VBGMM, mixture.DPGMM):
        model = m_constructor(n_components=n_comps, covariance_type='full',
                              min_covar=1e-7, n_iter=5,
                              random_state=np.random.RandomState(0))
        assert_fit_predict_correct(model, X)

    model = mixture.GMM(n_components=n_comps, n_iter=0)
    z = model.fit_predict(X)
    assert np.all(z == 0), "Quick Initialization Failed!"

def test_aic():
    # Test the aic and bic criteria
    n_samples, n_dim, n_components = 50, 3, 2
    X = rng.randn(n_samples, n_dim)
    SGH = 0.5 * (X.var() + np.log(2 * np.pi))  # standard gaussian entropy

    for cv_type in ['full', 'tied', 'diag', 'spherical']:
        g = mixture.GMM(n_components=n_components, covariance_type=cv_type,
                        random_state=rng, min_covar=1e-7)
        g.fit(X)
        aic = 2 * n_samples * SGH * n_dim + 2 * g._n_parameters()
        bic = (2 * n_samples * SGH * n_dim +
               np.log(n_samples) * g._n_parameters())
        bound = n_dim * 3. / np.sqrt(n_samples)
        assert_true(np.abs(g.aic(X) - aic) / n_samples < bound)
        assert_true(np.abs(g.bic(X) - bic) / n_samples < bound)

def check_positive_definite_covars(covariance_type):
    r"""Test that covariance matrices do not become non positive definite

    Due to the accumulation of round-off errors, the computation of the
    covariance  matrices during the learning phase could lead to non-positive
    definite covariance matrices. Namely the use of the formula:

    .. math:: C = (\sum_i w_i  x_i x_i^T) - \mu \mu^T

    instead of:

    .. math:: C = \sum_i w_i (x_i - \mu)(x_i - \mu)^T

    while mathematically equivalent, was observed a ``LinAlgError`` exception,
    when computing a ``GMM`` with full covariance matrices and fixed mean.

    This function ensures that some later optimization will not introduce the
    problem again.
    """
    rng = np.random.RandomState(1)
    # we build a dataset with 2 2d component. The components are unbalanced
    # (respective weights 0.9 and 0.1)
    X = rng.randn(100, 2)
    X[-10:] += (3, 3)  # Shift the 10 last points

    gmm = mixture.GMM(2, params="wc", covariance_type=covariance_type,
                      min_covar=1e-3)

    # This is a non-regression test for issue #2640. The following call used
    # to trigger:
    # numpy.linalg.linalg.LinAlgError: 2-th leading minor not positive definite
    gmm.fit(X)

    if covariance_type == "diag" or covariance_type == "spherical":
        assert_greater(gmm.covars_.min(), 0)
    else:
        if covariance_type == "tied":
            covs = [gmm.covars_]
        else:
            covs = gmm.covars_

        for c in covs:
            assert_greater(np.linalg.det(c), 0)

def test_positive_definite_covars():
    # Check positive definiteness for all covariance types
    for covariance_type in ["full", "tied", "diag", "spherical"]:
        yield check_positive_definite_covars, covariance_type

def test_verbose_first_level():
    # Create sample data
    X = rng.randn(30, 5)
    X[:10] += 2
    g = mixture.GMM(n_components=2, n_init=2, verbose=1)

    old_stdout = sys.stdout
    sys.stdout = StringIO()
    try:
        g.fit(X)
    finally:
        sys.stdout = old_stdout

def test_verbose_second_level():
    # Create sample data
    X = rng.randn(30, 5)
    X[:10] += 2
    g = mixture.GMM(n_components=2, n_init=2, verbose=2)

    old_stdout = sys.stdout
    sys.stdout = StringIO()
    try:
        g.fit(X)
    finally:
        sys.stdout = old_stdout