1086 lines
38 KiB
Python
1086 lines
38 KiB
Python
"""Gradient Boosted Regression Trees
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This module contains methods for fitting gradient boosted regression trees for
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both classification and regression.
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The module structure is the following:
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- The ``BaseGradientBoosting`` base class implements a common ``fit`` method
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for all the estimators in the module. Regression and classification
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only differ in the concrete ``LossFunction`` used.
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- ``GradientBoostingClassifier`` implements gradient boosting for
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classification problems.
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- ``GradientBoostingRegressor`` implements gradient boosting for
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regression problems.
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"""
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# Authors: Peter Prettenhofer, Scott White, Gilles Louppe, Emanuele Olivetti
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# License: BSD Style.
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from __future__ import print_function
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from __future__ import division
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from abc import ABCMeta, abstractmethod
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import sys
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import numpy as np
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from scipy import stats
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from .base import BaseEnsemble
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from ..base import BaseEstimator
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from ..base import ClassifierMixin
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from ..base import RegressorMixin
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from ..utils import check_random_state, array2d, check_arrays
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from ..utils.extmath import logsumexp
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from ..tree._tree import Tree
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from ..tree._tree import _random_sample_mask
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from ..tree._tree import MSE
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from ..tree._tree import DTYPE, TREE_LEAF, TREE_SPLIT_BEST
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from ._gradient_boosting import predict_stages
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from ._gradient_boosting import predict_stage
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class QuantileEstimator(BaseEstimator):
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"""An estimator predicting the alpha-quantile of the training targets."""
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def __init__(self, alpha=0.9):
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if not 0 < alpha < 1.0:
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raise ValueError("`alpha` must be in (0, 1.0)")
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self.alpha = alpha
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def fit(self, X, y):
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self.quantile = stats.scoreatpercentile(y, self.alpha * 100.0)
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def predict(self, X):
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y = np.empty((X.shape[0], 1), dtype=np.float64)
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y.fill(self.quantile)
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return y
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class MeanEstimator(BaseEstimator):
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"""An estimator predicting the mean of the training targets."""
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def fit(self, X, y):
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self.mean = np.mean(y)
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def predict(self, X):
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y = np.empty((X.shape[0], 1), dtype=np.float64)
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y.fill(self.mean)
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return y
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class LogOddsEstimator(BaseEstimator):
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"""An estimator predicting the log odds ratio."""
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def fit(self, X, y):
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n_pos = np.sum(y)
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self.prior = np.log(n_pos / (y.shape[0] - n_pos))
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def predict(self, X):
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y = np.empty((X.shape[0], 1), dtype=np.float64)
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y.fill(self.prior)
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return y
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class PriorProbabilityEstimator(BaseEstimator):
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"""An estimator predicting the probability of each
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class in the training data.
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"""
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def fit(self, X, y):
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class_counts = np.bincount(y)
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self.priors = class_counts / float(y.shape[0])
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def predict(self, X):
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y = np.empty((X.shape[0], self.priors.shape[0]), dtype=np.float64)
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y[:] = self.priors
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return y
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class LossFunction(object):
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"""Abstract base class for various loss functions.
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Attributes
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----------
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K : int
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The number of regression trees to be induced;
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1 for regression and binary classification;
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``n_classes`` for multi-class classification.
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"""
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__metaclass__ = ABCMeta
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is_multi_class = False
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def __init__(self, n_classes):
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self.K = n_classes
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def init_estimator(self, X, y):
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"""Default ``init`` estimator for loss function. """
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raise NotImplementedError()
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@abstractmethod
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def __call__(self, y, pred):
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"""Compute the loss of prediction ``pred`` and ``y``. """
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@abstractmethod
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def negative_gradient(self, y, y_pred, **kargs):
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"""Compute the negative gradient.
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Parameters
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---------
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y : np.ndarray, shape=(n,)
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The target labels.
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y_pred : np.ndarray, shape=(n,):
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The predictions.
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"""
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def update_terminal_regions(self, tree, X, y, residual, y_pred,
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sample_mask, learn_rate=1.0, k=0):
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"""Update the terminal regions (=leaves) of the given tree and
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updates the current predictions of the model. Traverses tree
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and invokes template method `_update_terminal_region`.
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Parameters
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----------
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tree : tree.Tree
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The tree object.
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X : np.ndarray, shape=(n, m)
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The data array.
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y : np.ndarray, shape=(n,)
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The target labels.
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residual : np.ndarray, shape=(n,)
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The residuals (usually the negative gradient).
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y_pred : np.ndarray, shape=(n,):
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The predictions.
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"""
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# compute leaf for each sample in ``X``.
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terminal_regions = tree.apply(X)
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# mask all which are not in sample mask.
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masked_terminal_regions = terminal_regions.copy()
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masked_terminal_regions[~sample_mask] = -1
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# update each leaf (= perform line search)
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for leaf in np.where(tree.children_left == TREE_LEAF)[0]:
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self._update_terminal_region(tree, masked_terminal_regions,
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leaf, X, y, residual,
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y_pred[:, k])
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# update predictions (both in-bag and out-of-bag)
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y_pred[:, k] += learn_rate * tree.value[:, 0, 0].take(terminal_regions,
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axis=0)
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@abstractmethod
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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"""Template method for updating terminal regions (=leaves). """
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class RegressionLossFunction(LossFunction):
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"""Base class for regression loss functions. """
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__metaclass__ = ABCMeta
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def __init__(self, n_classes):
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if n_classes != 1:
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raise ValueError("``n_classes`` must be 1 for regression")
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super(RegressionLossFunction, self).__init__(n_classes)
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class LeastSquaresError(RegressionLossFunction):
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"""Loss function for least squares (LS) estimation.
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Terminal regions need not to be updated for least squares. """
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def init_estimator(self):
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return MeanEstimator()
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def __call__(self, y, pred):
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return np.mean((y - pred.ravel()) ** 2.0)
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def negative_gradient(self, y, pred, **kargs):
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return y - pred.ravel()
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def update_terminal_regions(self, tree, X, y, residual, y_pred,
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sample_mask, learn_rate=1.0, k=0):
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"""Least squares does not need to update terminal regions.
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But it has to update the predictions.
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"""
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# update predictions
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y_pred[:, k] += learn_rate * tree.predict(X).ravel()
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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pass
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class LeastAbsoluteError(RegressionLossFunction):
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"""Loss function for least absolute deviation (LAD) regression. """
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def init_estimator(self):
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return QuantileEstimator(alpha=0.5)
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def __call__(self, y, pred):
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return np.abs(y - pred.ravel()).mean()
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def negative_gradient(self, y, pred, **kargs):
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"""1.0 if y - pred > 0.0 else -1.0"""
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pred = pred.ravel()
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return 2.0 * (y - pred > 0.0) - 1.0
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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"""LAD updates terminal regions to median estimates. """
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terminal_region = np.where(terminal_regions == leaf)[0]
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tree.value[leaf, 0, 0] = np.median(y.take(terminal_region, axis=0) - \
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pred.take(terminal_region, axis=0))
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class HuberLossFunction(RegressionLossFunction):
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"""Loss function for least absolute deviation (LAD) regression. """
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def __init__(self, n_classes, alpha=0.9):
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super(HuberLossFunction, self).__init__(n_classes)
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self.alpha = alpha
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def init_estimator(self):
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return QuantileEstimator(alpha=0.5)
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def __call__(self, y, pred):
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pred = pred.ravel()
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diff = y - pred
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gamma = self.gamma
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gamma_mask = np.abs(diff) <= gamma
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sq_loss = np.sum(0.5 * diff[gamma_mask] ** 2.0)
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lin_loss = np.sum(gamma * (np.abs(diff[~gamma_mask]) - gamma / 2.0))
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return (sq_loss + lin_loss) / y.shape[0]
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def negative_gradient(self, y, pred, **kargs):
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pred = pred.ravel()
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diff = y - pred
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gamma = stats.scoreatpercentile(np.abs(diff), self.alpha * 100)
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gamma_mask = np.abs(diff) <= gamma
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residual = np.zeros((y.shape[0],), dtype=np.float64)
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residual[gamma_mask] = diff[gamma_mask]
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residual[~gamma_mask] = gamma * np.sign(diff[~gamma_mask])
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self.gamma = gamma
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return residual
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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"""LAD updates terminal regions to median estimates. """
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terminal_region = np.where(terminal_regions == leaf)[0]
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gamma = self.gamma
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diff = y.take(terminal_region, axis=0) - \
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pred.take(terminal_region, axis=0)
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median = np.median(diff)
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diff_minus_median = diff - median
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tree.value[leaf, 0] = median + np.mean(
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np.sign(diff_minus_median) *
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np.minimum(np.abs(diff_minus_median), gamma))
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class QuantileLossFunction(RegressionLossFunction):
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"""Loss function for quantile regression.
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Quantile regression allows to estimate the percentiles
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of the conditional distribution of the target.
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"""
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def __init__(self, n_classes, alpha=0.9):
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super(QuantileLossFunction, self).__init__(n_classes)
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assert 0 < alpha < 1.0
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self.alpha = alpha
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self.percentile = alpha * 100.0
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def init_estimator(self):
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return QuantileEstimator(self.alpha)
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def __call__(self, y, pred):
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pred = pred.ravel()
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diff = y - pred
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alpha = self.alpha
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mask = y > pred
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return (alpha * diff[mask].sum() +
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(1.0 - alpha) * diff[~mask].sum()) / y.shape[0]
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def negative_gradient(self, y, pred, **kargs):
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alpha = self.alpha
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pred = pred.ravel()
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mask = y > pred
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return (alpha * mask) - ((1.0 - alpha) * ~mask)
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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"""LAD updates terminal regions to median estimates. """
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terminal_region = np.where(terminal_regions == leaf)[0]
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diff = y.take(terminal_region, axis=0) - \
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pred.take(terminal_region, axis=0)
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val = stats.scoreatpercentile(diff, self.percentile)
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tree.value[leaf, 0] = val
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class BinomialDeviance(LossFunction):
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"""Binomial deviance loss function for binary classification.
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Binary classification is a special case; here, we only need to
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fit one tree instead of ``n_classes`` trees.
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"""
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def __init__(self, n_classes):
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if n_classes != 2:
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raise ValueError("%s requires 2 classes." %
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self.__class__.__name__)
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# we only need to fit one tree for binary clf.
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super(BinomialDeviance, self).__init__(1)
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def init_estimator(self):
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return LogOddsEstimator()
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def __call__(self, y, pred):
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"""Compute the deviance (= negative log-likelihood). """
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# logaddexp(0, v) == log(1.0 + exp(v))
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pred = pred.ravel()
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return np.sum(np.logaddexp(0.0, -2 * y * pred)) / y.shape[0]
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def negative_gradient(self, y, pred, **kargs):
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return y - 1.0 / (1.0 + np.exp(-pred.ravel()))
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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"""Make a single Newton-Raphson step. """
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terminal_region = np.where(terminal_regions == leaf)[0]
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residual = residual.take(terminal_region, axis=0)
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y = y.take(terminal_region, axis=0)
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numerator = residual.sum()
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denominator = np.sum((y - residual) * (1 - y + residual))
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if denominator == 0.0:
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tree.value[leaf, 0, 0] = 0.0
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else:
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tree.value[leaf, 0, 0] = numerator / denominator
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class MultinomialDeviance(LossFunction):
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"""Multinomial deviance loss function for multi-class classification.
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For multi-class classification we need to fit ``n_classes`` trees at
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each stage.
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"""
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is_multi_class = True
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def __init__(self, n_classes):
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if n_classes < 3:
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raise ValueError("%s requires more than 2 classes."
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% self.__class__.__name__)
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super(MultinomialDeviance, self).__init__(n_classes)
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def init_estimator(self):
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return PriorProbabilityEstimator()
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def __call__(self, y, pred):
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# create one-hot label encoding
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Y = np.zeros((y.shape[0], self.K), dtype=np.float64)
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for k in range(self.K):
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Y[:, k] = y == k
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return np.sum(-1 * (Y * pred).sum(axis=1) +
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logsumexp(pred, axis=1))
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def negative_gradient(self, y, pred, k=0):
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"""Compute negative gradient for the ``k``-th class. """
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return y - np.nan_to_num(np.exp(pred[:, k] -
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logsumexp(pred, axis=1)))
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def _update_terminal_region(self, tree, terminal_regions, leaf, X, y,
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residual, pred):
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"""Make a single Newton-Raphson step. """
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terminal_region = np.where(terminal_regions == leaf)[0]
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residual = residual.take(terminal_region, axis=0)
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y = y.take(terminal_region, axis=0)
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numerator = residual.sum()
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numerator *= (self.K - 1) / self.K
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denominator = np.sum((y - residual) * (1.0 - y + residual))
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if denominator == 0.0:
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tree.value[leaf, 0, 0] = 0.0
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else:
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tree.value[leaf, 0, 0] = numerator / denominator
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LOSS_FUNCTIONS = {'ls': LeastSquaresError,
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'lad': LeastAbsoluteError,
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'huber': HuberLossFunction,
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'quantile': QuantileLossFunction,
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'bdeviance': BinomialDeviance,
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'mdeviance': MultinomialDeviance,
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'deviance': None} # for both, multinomial and binomial
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class BaseGradientBoosting(BaseEnsemble):
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"""Abstract base class for Gradient Boosting. """
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__metaclass__ = ABCMeta
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@abstractmethod
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def __init__(self, loss, learn_rate, n_estimators, min_samples_split,
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min_samples_leaf, max_depth, init, subsample,
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max_features, random_state, alpha=0.9, verbose=0):
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if n_estimators <= 0:
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raise ValueError("n_estimators must be greater than 0")
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self.n_estimators = n_estimators
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if learn_rate <= 0.0:
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raise ValueError("learn_rate must be greater than 0")
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self.learn_rate = learn_rate
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if loss not in LOSS_FUNCTIONS:
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raise ValueError("Loss '%s' not supported. " % loss)
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self.loss = loss
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if min_samples_split <= 0:
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raise ValueError("min_samples_split must be larger than 0")
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self.min_samples_split = min_samples_split
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if min_samples_leaf <= 0:
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raise ValueError("min_samples_leaf must be larger than 0")
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self.min_samples_leaf = min_samples_leaf
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if subsample <= 0.0 or subsample > 1:
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raise ValueError("subsample must be in (0,1]")
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self.subsample = subsample
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self.max_features = max_features
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if max_depth <= 0:
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raise ValueError("max_depth must be larger than 0")
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self.max_depth = max_depth
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if init is not None:
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if not hasattr(init, 'fit') or not hasattr(init, 'predict'):
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raise ValueError("init must be valid estimator")
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self.init = init
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self.random_state = check_random_state(random_state)
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if not (0.0 < alpha < 1.0):
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raise ValueError("alpha must be in (0.0, 1.0)")
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self.alpha = alpha
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self.verbose = verbose
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self.estimators_ = None
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def fit_stage(self, i, X, X_argsorted, y, y_pred, sample_mask):
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"""Fit another stage of ``n_classes_`` trees to the boosting model. """
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loss = self.loss_
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original_y = y
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for k in range(loss.K):
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if loss.is_multi_class:
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y = np.array(original_y == k, dtype=np.float64)
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residual = loss.negative_gradient(y, y_pred, k=k)
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# induce regression tree on residuals
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tree = Tree(self.n_features, (1,), 1, MSE(1), self.max_depth,
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self.min_samples_split, self.min_samples_leaf, 0.0,
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self.max_features, TREE_SPLIT_BEST, self.random_state)
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tree.build(X, residual[:, np.newaxis], sample_mask, X_argsorted)
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# update tree leaves
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self.loss_.update_terminal_regions(tree, X, y, residual, y_pred,
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sample_mask, self.learn_rate,
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k=k)
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# add tree to ensemble
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self.estimators_[i, k] = tree
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return y_pred
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def fit(self, X, y):
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"""Fit the gradient boosting model.
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Parameters
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----------
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X : array-like, shape = [n_samples, n_features]
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Training vectors, where n_samples is the number of samples
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and n_features is the number of features. Use fortran-style
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to avoid memory copies.
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y : array-like, shape = [n_samples]
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Target values (integers in classification, real numbers in
|
|
regression)
|
|
For classification, labels must correspond to classes
|
|
``0, 1, ..., n_classes_-1``
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
X, y = check_arrays(X, y, sparse_format='dense')
|
|
X = np.asfortranarray(X, dtype=DTYPE)
|
|
y = np.ravel(y, order='C')
|
|
|
|
n_samples, n_features = X.shape
|
|
self.n_features = n_features
|
|
|
|
if self.max_features is None:
|
|
self.max_features = n_features
|
|
|
|
if not (0 < self.max_features <= n_features):
|
|
raise ValueError("max_features must be in (0, n_features]")
|
|
|
|
loss_class = LOSS_FUNCTIONS[self.loss]
|
|
if self.loss in ('huber', 'quantile'):
|
|
loss = loss_class(self.n_classes_, self.alpha)
|
|
else:
|
|
loss = loss_class(self.n_classes_)
|
|
|
|
# store loss object for future use
|
|
self.loss_ = loss
|
|
|
|
if self.init is None:
|
|
self.init = loss.init_estimator()
|
|
|
|
# create argsorted X for fast tree induction
|
|
X_argsorted = np.asfortranarray(
|
|
np.argsort(X.T, axis=1).astype(np.int32).T)
|
|
|
|
# fit initial model
|
|
self.init.fit(X, y)
|
|
|
|
# init predictions
|
|
y_pred = self.init.predict(X)
|
|
|
|
self.estimators_ = np.empty((self.n_estimators, loss.K),
|
|
dtype=np.object)
|
|
|
|
self.train_score_ = np.zeros((self.n_estimators,), dtype=np.float64)
|
|
self.oob_score_ = np.zeros((self.n_estimators), dtype=np.float64)
|
|
|
|
sample_mask = np.ones((n_samples,), dtype=np.bool)
|
|
n_inbag = max(1, int(self.subsample * n_samples))
|
|
|
|
# perform boosting iterations
|
|
for i in range(self.n_estimators):
|
|
|
|
# subsampling
|
|
if self.subsample < 1.0:
|
|
# TODO replace with ``np.choice`` if possible.
|
|
sample_mask = _random_sample_mask(n_samples, n_inbag,
|
|
self.random_state)
|
|
# fit next stage of trees
|
|
y_pred = self.fit_stage(i, X, X_argsorted, y, y_pred, sample_mask)
|
|
|
|
# track deviance (= loss)
|
|
if self.subsample < 1.0:
|
|
self.train_score_[i] = loss(y[sample_mask],
|
|
y_pred[sample_mask])
|
|
self.oob_score_[i] = loss(y[~sample_mask],
|
|
y_pred[~sample_mask])
|
|
if self.verbose > 1:
|
|
print("built tree %d of %d, train score = %.6e, "
|
|
"oob score = %.6e" % (i + 1, self.n_estimators,
|
|
self.train_score_[i], self.oob_score_[i]))
|
|
else:
|
|
# no need to fancy index w/ no subsampling
|
|
self.train_score_[i] = loss(y, y_pred)
|
|
if self.verbose > 1:
|
|
print("built tree %d of %d, train score = %.6e" %
|
|
(i + 1, self.n_estimators, self.train_score_[i]))
|
|
if self.verbose == 1:
|
|
print(end='.')
|
|
sys.stdout.flush()
|
|
|
|
return self
|
|
|
|
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``. """
|
|
if self.estimators_ is None or len(self.estimators_) == 0:
|
|
raise ValueError("Estimator not fitted, call `fit` " \
|
|
"before making predictions`.")
|
|
if X.shape[1] != self.n_features:
|
|
raise ValueError("X.shape[1] should be %d, not %d." %
|
|
(self.n_features, X.shape[1]))
|
|
score = self.init.predict(X).astype(np.float64)
|
|
return score
|
|
|
|
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, k]
|
|
The decision function of the input samples. Classes are
|
|
ordered by arithmetical order. Regression and binary
|
|
classification are special cases with ``k == 1``,
|
|
otherwise ``k==n_classes``.
|
|
"""
|
|
X = array2d(X, dtype=DTYPE, order='C')
|
|
score = self._init_decision_function(X)
|
|
predict_stages(self.estimators_, X, self.learn_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 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. Classes are
|
|
ordered by arithmetical order. Regression and binary
|
|
classification are special cases with ``k == 1``,
|
|
otherwise ``k==n_classes``.
|
|
"""
|
|
X = array2d(X, dtype=DTYPE, order='C')
|
|
score = self._init_decision_function(X)
|
|
for i in range(self.n_estimators):
|
|
predict_stage(self.estimators_, i, X, self.learn_rate, score)
|
|
yield score
|
|
|
|
@property
|
|
def feature_importances_(self):
|
|
if self.estimators_ is None or len(self.estimators_) == 0:
|
|
raise ValueError("Estimator not fitted, " \
|
|
"call `fit` before `feature_importances_`.")
|
|
total_sum = np.zeros((self.n_features, ), dtype=np.float64)
|
|
for stage in self.estimators_:
|
|
stage_sum = sum(tree.compute_feature_importances(method='gini')
|
|
for tree in stage) / len(stage)
|
|
total_sum += stage_sum
|
|
|
|
importances = total_sum / len(self.estimators_)
|
|
return importances
|
|
|
|
|
|
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.
|
|
|
|
Parameters
|
|
----------
|
|
loss : {'deviance'}, optional (default='deviance')
|
|
loss function to be optimized. 'deviance' refers to
|
|
deviance (= logistic regression) for classification
|
|
with probabilistic outputs.
|
|
|
|
learn_rate : float, optional (default=0.1)
|
|
learning rate shrinks the contribution of each tree by `learn_rate`.
|
|
There is a trade-off between learn_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.
|
|
|
|
min_samples_split : integer, optional (default=1)
|
|
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.
|
|
|
|
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, None, optional (default=None)
|
|
The number of features to consider when looking for the best split.
|
|
Features are choosen randomly at each split point.
|
|
If None, then `max_features=n_features`. Choosing
|
|
`max_features < n_features` leads to a reduction of variance
|
|
and an increase in bias.
|
|
|
|
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 '.' for every tree built.
|
|
If greater than 1 then it prints the score for every tree.
|
|
|
|
Attributes
|
|
----------
|
|
`feature_importances_` : array, shape = [n_features]
|
|
The feature importances (the higher, the more important the feature).
|
|
|
|
`oob_score_` : array, shape = [n_estimators]
|
|
Score of the training dataset obtained using an out-of-bag estimate.
|
|
The i-th score ``oob_score_[i]`` is the deviance (= loss) of the
|
|
model at iteration ``i`` on the out-of-bag sample.
|
|
|
|
`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``.
|
|
|
|
Examples
|
|
--------
|
|
>>> samples = [[0, 0, 2], [1, 0, 0]]
|
|
>>> labels = [0, 1]
|
|
>>> from sklearn.ensemble import GradientBoostingClassifier
|
|
>>> gb = GradientBoostingClassifier().fit(samples, labels)
|
|
>>> print(gb.predict([[0.5, 0, 0]]))
|
|
[0]
|
|
|
|
See also
|
|
--------
|
|
sklearn.tree.DecisionTreeClassifier, RandomForestClassifier
|
|
|
|
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.
|
|
"""
|
|
|
|
def __init__(self, loss='deviance', learn_rate=0.1, n_estimators=100,
|
|
subsample=1.0, min_samples_split=1, min_samples_leaf=1,
|
|
max_depth=3, init=None, random_state=None,
|
|
max_features=None, verbose=0):
|
|
|
|
super(GradientBoostingClassifier, self).__init__(
|
|
loss, learn_rate, n_estimators, min_samples_split,
|
|
min_samples_leaf, max_depth, init, subsample, max_features,
|
|
random_state, verbose=verbose)
|
|
|
|
def fit(self, X, y):
|
|
"""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. Use fortran-style
|
|
to avoid memory copies.
|
|
|
|
y : array-like, shape = [n_samples]
|
|
Target values (integers in classification, real numbers in
|
|
regression)
|
|
For classification, labels must correspond to classes
|
|
``0, 1, ..., n_classes_-1``
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
self.classes_ = np.unique(y)
|
|
self.n_classes_ = len(self.classes_)
|
|
y = np.searchsorted(self.classes_, y)
|
|
if self.loss == 'deviance':
|
|
self.loss = 'mdeviance' if len(self.classes_) > 2 else 'bdeviance'
|
|
|
|
return super(GradientBoostingClassifier, self).fit(X, y)
|
|
|
|
def _score_to_proba(self, score):
|
|
"""Compute class probability estimates from decision scores. """
|
|
proba = np.ones((score.shape[0], self.n_classes_), dtype=np.float64)
|
|
if not self.loss_.is_multi_class:
|
|
proba[:, 1] = 1.0 / (1.0 + np.exp(-score.ravel()))
|
|
proba[:, 0] -= proba[:, 1]
|
|
else:
|
|
proba = np.nan_to_num(
|
|
np.exp(score - (logsumexp(score, axis=1)[:, np.newaxis])))
|
|
return proba
|
|
|
|
def predict_proba(self, X):
|
|
"""Predict class probabilities for X.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape = [n_samples, n_features]
|
|
The input samples.
|
|
|
|
Returns
|
|
-------
|
|
p : array of shape = [n_samples]
|
|
The class probabilities of the input samples. Classes are
|
|
ordered by arithmetical order.
|
|
"""
|
|
score = self.decision_function(X)
|
|
return self._score_to_proba(score)
|
|
|
|
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 : array of shape = [n_samples]
|
|
The predicted value of the input samples.
|
|
"""
|
|
for score in self.staged_decision_function(X):
|
|
yield self._score_to_proba(X)
|
|
|
|
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 classes.
|
|
"""
|
|
proba = self.predict_proba(X)
|
|
return self.classes_.take(np.argmax(proba, axis=1), axis=0)
|
|
|
|
def staged_predict(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 : array of shape = [n_samples]
|
|
The predicted value of the input samples.
|
|
"""
|
|
for proba in self.staged_predict_proba(X):
|
|
yield self.classes_.take(np.argmax(proba, axis=1), axis=0)
|
|
|
|
|
|
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.
|
|
|
|
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 soley 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).
|
|
|
|
learn_rate : float, optional (default=0.1)
|
|
learning rate shrinks the contribution of each tree by `learn_rate`.
|
|
There is a trade-off between learn_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.
|
|
|
|
min_samples_split : integer, optional (default=1)
|
|
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.
|
|
|
|
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, None, optional (default=None)
|
|
The number of features to consider when looking for the best split.
|
|
Features are choosen randomly at each split point.
|
|
If None, then `max_features=n_features`. Choosing
|
|
`max_features < n_features` leads to a reduction of variance
|
|
and an increase in bias.
|
|
|
|
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 '.' for every tree built.
|
|
If greater than 1 then it prints the score for every tree.
|
|
|
|
Attributes
|
|
----------
|
|
`feature_importances_` : array, shape = [n_features]
|
|
The feature importances (the higher, the more important the feature).
|
|
|
|
`oob_score_` : array, shape = [n_estimators]
|
|
Score of the training dataset obtained using an out-of-bag estimate.
|
|
The i-th score ``oob_score_[i]`` is the deviance (= loss) of the
|
|
model at iteration ``i`` on the out-of-bag sample.
|
|
|
|
`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``.
|
|
|
|
Examples
|
|
--------
|
|
>>> samples = [[0, 0, 2], [1, 0, 0]]
|
|
>>> labels = [0, 1]
|
|
>>> from sklearn.ensemble import GradientBoostingRegressor
|
|
>>> gb = GradientBoostingRegressor().fit(samples, labels)
|
|
>>> print(gb.predict([[0, 0, 0]]))
|
|
... # doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
|
|
[ 1.32806...
|
|
|
|
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.
|
|
"""
|
|
|
|
def __init__(self, loss='ls', learn_rate=0.1, n_estimators=100,
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|
subsample=1.0, min_samples_split=1, min_samples_leaf=1,
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|
max_depth=3, init=None, random_state=None,
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|
max_features=None, alpha=0.9, verbose=0):
|
|
|
|
super(GradientBoostingRegressor, self).__init__(
|
|
loss, learn_rate, n_estimators, min_samples_split,
|
|
min_samples_leaf, max_depth, init, subsample, max_features,
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|
random_state, alpha, verbose)
|
|
|
|
def fit(self, X, y):
|
|
"""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. Use fortran-style
|
|
to avoid memory copies.
|
|
|
|
y : array-like, shape = [n_samples]
|
|
Target values (integers in classification, real numbers in
|
|
regression)
|
|
For classification, labels must correspond to classes
|
|
``0, 1, ..., n_classes_-1``
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns self.
|
|
"""
|
|
self.n_classes_ = 1
|
|
return super(GradientBoostingRegressor, self).fit(X, y)
|
|
|
|
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.
|
|
"""
|
|
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 : array of shape = [n_samples]
|
|
The predicted value of the input samples.
|
|
"""
|
|
for y in self.staged_decision_function(X):
|
|
yield y.ravel()
|