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1822 1823 1824 | """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 ..feature_selection.from_model import _LearntSelectorMixin
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 import deprecated
from ..utils.extmath import logsumexp
from ..utils.fixes import expit
from ..utils.fixes import bincount
from ..utils.stats import _weighted_percentile
from ..utils.validation import check_is_fitted
from ..utils.validation import NotFittedError
from ..utils.multiclass import check_classification_targets
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,
_LearntSelectorMixin)):
"""Abstract base class for Gradient Boosting. """
@abstractmethod
def __init__(self, loss, learning_rate, n_estimators, min_samples_split,
min_samples_leaf, min_weight_fraction_leaf,
max_depth, 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.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.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
self.estimators_ = np.empty((0, 0), dtype=np.object)
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='friedman_mse',
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,
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."""
if self.estimators_ is None or len(self.estimators_) == 0:
raise NotFittedError("Estimator not fitted, call `fit`"
" before making predictions`.")
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 self.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
@deprecated(" and will be removed in 0.19")
def decision_function(self, X):
"""Compute the decision function of ``X``.
Parameters
----------
X : array-like of shape = [n_samples, n_features]
The input samples.
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].
"""
self._check_initialized()
X = self.estimators_[0, 0]._validate_X_predict(X, check_input=True)
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 of shape = [n_samples, n_features]
The input samples.
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")
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()
@deprecated(" and will be removed in 0.19")
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 of shape = [n_samples, n_features]
The input samples.
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
@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, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
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 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.
Ignored if ``max_leaf_nodes`` is not None.
min_samples_split : integer, optional (default=2)
The minimum number of samples required to split an internal node.
min_samples_leaf : integer, optional (default=1)
The minimum number of samples required to be at a leaf node.
min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the input samples required to be at a
leaf node.
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.
If not None then ``max_depth`` will be ignored.
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, min_samples_split=2,
min_samples_leaf=1, min_weight_fraction_leaf=0.,
max_depth=3, 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,
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, 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 of shape = [n_samples, n_features]
The input samples.
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")
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 of shape = [n_samples, n_features]
The input samples.
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 of shape = [n_samples, n_features]
The input samples.
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 of shape = [n_samples, n_features]
The input samples.
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 of shape = [n_samples, n_features]
The input samples.
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 of shape = [n_samples, n_features]
The input samples.
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 of shape = [n_samples, n_features]
The input samples.
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.
Ignored if ``max_leaf_nodes`` is not None.
min_samples_split : integer, optional (default=2)
The minimum number of samples required to split an internal node.
min_samples_leaf : integer, optional (default=1)
The minimum number of samples required to be at a leaf node.
min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the input samples required to be at a
leaf node.
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.
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, min_samples_split=2,
min_samples_leaf=1, min_weight_fraction_leaf=0.,
max_depth=3, 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,
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, alpha=alpha, verbose=verbose,
max_leaf_nodes=max_leaf_nodes, warm_start=warm_start,
presort='auto')
def predict(self, X):
"""Predict regression target for X.
Parameters
----------
X : array-like of shape = [n_samples, n_features]
The input samples.
Returns
-------
y : array of shape = [n_samples]
The predicted values.
"""
X = check_array(X, dtype=DTYPE, order="C")
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 of shape = [n_samples, n_features]
The input samples.
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, it will be converted to
``dtype=np.float32`` and if a sparse matrix is provided
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 in each estimator.
"""
leaves = super(GradientBoostingRegressor, self).apply(X)
leaves = leaves.reshape(X.shape[0], self.estimators_.shape[0])
return leaves
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