1204 lines
44 KiB
Python
1204 lines
44 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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# Arnaud Joly
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# License: BSD 3 clause
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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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from warnings import warn
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from time import time
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import numbers
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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, column_or_1d
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from ..utils.extmath import logsumexp
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from ..utils.fixes import unique
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from ..externals import six
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from ..tree.tree import DecisionTreeRegressor
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from ..tree._tree import DTYPE, TREE_LEAF
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from ..tree._tree import MSE, PresortBestSplitter
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from ._gradient_boosting import predict_stages
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from ._gradient_boosting import predict_stage
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from ._gradient_boosting import _random_sample_mask
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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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n_neg = y.shape[0] - n_pos
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if n_neg == 0 or n_pos == 0:
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raise ValueError('y contains non binary labels.')
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self.prior = np.log(n_pos / n_neg)
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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(six.with_metaclass(ABCMeta, 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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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, learning_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] += (learning_rate
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* tree.value[:, 0, 0].take(terminal_regions, 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(six.with_metaclass(ABCMeta, LossFunction)):
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"""Base class for regression loss functions. """
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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, learning_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] += learning_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("{0:s} requires 2 classes.".format(
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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 (= 2 * 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 -2.0 * np.mean((y * pred) - np.logaddexp(0.0, pred))
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def negative_gradient(self, y, pred, **kargs):
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"""Compute the residual (= negative gradient). """
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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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our node estimate is given by:
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sum(y - prob) / sum(prob * (1 - prob))
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we take advantage that: y - prob = residual
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"""
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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("{0:s} requires more than 2 classes.".format(
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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(six.with_metaclass(ABCMeta, BaseEnsemble)):
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"""Abstract base class for Gradient Boosting. """
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@abstractmethod
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def __init__(self, loss, learning_rate, n_estimators, min_samples_split,
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min_samples_leaf, max_depth, init, subsample, max_features,
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random_state, alpha=0.9, verbose=0):
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self.n_estimators = n_estimators
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self.learning_rate = learning_rate
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self.loss = loss
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self.min_samples_split = min_samples_split
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self.min_samples_leaf = min_samples_leaf
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self.subsample = subsample
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self.max_features = max_features
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self.max_depth = max_depth
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self.init = init
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self.random_state = random_state
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self.alpha = alpha
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self.verbose = verbose
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self.estimators_ = np.empty((0, 0), dtype=np.object)
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def _fit_stage(self, i, X, y, y_pred, sample_mask,
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criterion, splitter, random_state):
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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 = DecisionTreeRegressor(
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criterion=criterion,
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splitter=splitter,
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max_depth=self.max_depth,
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min_samples_split=self.min_samples_split,
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min_samples_leaf=self.min_samples_leaf,
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max_features=self.max_features,
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random_state=random_state)
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sample_weight = None
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if self.subsample < 1.0:
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sample_weight = sample_mask.astype(np.float64)
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tree.fit(X, residual,
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sample_weight=sample_weight, check_input=False)
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# update tree leaves
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loss.update_terminal_regions(tree.tree_, X, y, residual, y_pred,
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sample_mask, self.learning_rate, 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 _check_params(self):
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"""Check validity of parameters and raise ValueError if not valid. """
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if self.n_estimators <= 0:
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raise ValueError("n_estimators must be greater than 0")
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if self.learning_rate <= 0.0:
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raise ValueError("learning_rate must be greater than 0")
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if (self.loss not in self._SUPPORTED_LOSS or
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self.loss not in LOSS_FUNCTIONS):
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raise ValueError("Loss '{0:s}' not supported. ".format(self.loss))
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if self.loss in ('mdeviance', 'bdeviance'):
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warn(("Loss '{0:s}' is deprecated as of version 0.14. "
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"Use 'deviance' instead. ").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 self.subsample <= 0.0 or self.subsample > 1:
|
|
raise ValueError("subsample must be in (0,1]")
|
|
|
|
if self.init is not None:
|
|
if (not hasattr(self.init, 'fit')
|
|
or not hasattr(self.init, 'predict')):
|
|
raise ValueError("init must be valid estimator")
|
|
self.init_ = self.init
|
|
else:
|
|
self.init_ = self.loss_.init_estimator()
|
|
|
|
if not (0.0 < self.alpha and self.alpha < 1.0):
|
|
raise ValueError("alpha must be in (0.0, 1.0)")
|
|
|
|
if isinstance(self.max_features, six.string_types):
|
|
if self.max_features == "auto":
|
|
if is_classification:
|
|
max_features = max(1, int(np.sqrt(self.n_features)))
|
|
else:
|
|
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. Allowed string '
|
|
'values are "auto", "sqrt" or "log2".')
|
|
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
|
|
max_features = int(self.max_features * self.n_features)
|
|
|
|
self.max_features_ = max_features
|
|
|
|
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.
|
|
|
|
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.
|
|
"""
|
|
# Check input
|
|
X, = check_arrays(X, dtype=DTYPE, sparse_format="dense",
|
|
check_ccontiguous=True)
|
|
y = column_or_1d(y, warn=True)
|
|
n_samples, n_features = X.shape
|
|
self.n_features = n_features
|
|
random_state = check_random_state(self.random_state)
|
|
|
|
# Check parameters
|
|
self._check_params()
|
|
|
|
# pull freq used parameters into local scope
|
|
subsample = self.subsample
|
|
loss_ = self.loss_
|
|
do_oob = subsample < 1.0
|
|
|
|
# allocate model state data structures
|
|
self.estimators_ = np.empty((self.n_estimators, self.loss_.K),
|
|
dtype=np.object)
|
|
self.train_score_ = np.zeros((self.n_estimators,), dtype=np.float64)
|
|
if do_oob:
|
|
self._oob_score_ = np.zeros((self.n_estimators), dtype=np.float64)
|
|
self.oob_improvement_ = np.zeros((self.n_estimators),
|
|
dtype=np.float64)
|
|
|
|
sample_mask = np.ones((n_samples,), dtype=np.bool)
|
|
n_inbag = max(1, int(subsample * n_samples))
|
|
|
|
if self.verbose:
|
|
# header fields and line format str
|
|
header_fields = ['Iter', 'Train Loss']
|
|
verbose_fmt = ['{iter:>10d}', '{train_score:>16.4f}']
|
|
if do_oob:
|
|
header_fields.append('OOB Improve')
|
|
verbose_fmt.append('{oob_impr:>16.4f}')
|
|
header_fields.append('Remaining Time')
|
|
verbose_fmt.append('{remaining_time:>16s}')
|
|
verbose_fmt = ' '.join(verbose_fmt)
|
|
# print the header line
|
|
print(('%10s ' + '%16s ' *
|
|
(len(header_fields) - 1)) % tuple(header_fields))
|
|
# plot verbose info each time i % verbose_mod == 0
|
|
verbose_mod = 1
|
|
start_time = time()
|
|
|
|
# fit initial model
|
|
self.init_.fit(X, y)
|
|
|
|
# init predictions
|
|
y_pred = self.init_.predict(X)
|
|
|
|
# init criterion and splitter
|
|
criterion = MSE(1)
|
|
splitter = PresortBestSplitter(criterion,
|
|
self.max_features_,
|
|
self.min_samples_leaf,
|
|
random_state)
|
|
|
|
# perform boosting iterations
|
|
for i in range(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])
|
|
|
|
# fit next stage of trees
|
|
y_pred = self._fit_stage(i, X, y, y_pred, sample_mask,
|
|
criterion, splitter, random_state)
|
|
|
|
# track deviance (= loss)
|
|
if do_oob:
|
|
self.train_score_[i] = loss_(y[sample_mask],
|
|
y_pred[sample_mask])
|
|
self._oob_score_[i] = loss_(y[~sample_mask],
|
|
y_pred[~sample_mask])
|
|
self.oob_improvement_[i] = old_oob_score - self._oob_score_[i]
|
|
else:
|
|
# no need to fancy index w/ no subsampling
|
|
self.train_score_[i] = self.loss_(y, y_pred)
|
|
|
|
if self.verbose > 0:
|
|
if (i + 1) % verbose_mod == 0:
|
|
oob_impr = self.oob_improvement_[i] if do_oob else 0
|
|
remaining_time = ((self.n_estimators - (i + 1)) *
|
|
(time() - 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(verbose_fmt.format(iter=i + 1,
|
|
train_score=self.train_score_[i],
|
|
oob_impr=oob_impr,
|
|
remaining_time=remaining_time))
|
|
if self.verbose == 1 and ((i + 1) // (verbose_mod * 10) > 0):
|
|
# adjust verbose frequency (powers of 10)
|
|
verbose_mod *= 10
|
|
|
|
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 {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):
|
|
"""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.learning_rate, score)
|
|
return score
|
|
|
|
def staged_decision_function(self, X):
|
|
"""Compute decision function of ``X`` for each iteration.
|
|
|
|
This method allows monitoring (i.e. determine error on testing set)
|
|
after each stage.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like 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.learning_rate, score)
|
|
yield score
|
|
|
|
@property
|
|
def feature_importances_(self):
|
|
"""Return the feature importances (the higher, the more important the
|
|
feature).
|
|
|
|
Returns
|
|
-------
|
|
feature_importances_ : array, shape = [n_features]
|
|
"""
|
|
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.feature_importances_
|
|
for tree in stage) / len(stage)
|
|
total_sum += stage_sum
|
|
|
|
importances = total_sum / len(self.estimators_)
|
|
return importances
|
|
|
|
@property
|
|
def oob_score_(self):
|
|
warn("The oob_score_ argument is replaced by oob_improvement_"
|
|
" as of version 0.14 and will be removed in 0.16.",
|
|
DeprecationWarning)
|
|
try:
|
|
return self._oob_score_
|
|
except AttributeError:
|
|
raise ValueError("Estimator not fitted, "
|
|
"call `fit` before `oob_score_`.")
|
|
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
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="auto")
|
|
The number of features to consider when looking for the best split:
|
|
- If int, then consider `max_features` features at each split.
|
|
- If float, then `max_features` is a percentage and
|
|
`int(max_features * n_features)` features are considered at each
|
|
split.
|
|
- If "auto", then `max_features=sqrt(n_features)`.
|
|
- If "sqrt", then `max_features=sqrt(n_features)`.
|
|
- If "log2", then `max_features=log2(n_features)`.
|
|
- If None, then `max_features=n_features`.
|
|
|
|
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 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.
|
|
|
|
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.
|
|
|
|
`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.
|
|
Deprecated: use `oob_improvement_` instead.
|
|
|
|
`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_`: list of DecisionTreeRegressor
|
|
The collection of fitted sub-estimators.
|
|
|
|
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.
|
|
"""
|
|
|
|
_SUPPORTED_LOSS = ('deviance', 'mdeviance', 'bdeviance')
|
|
|
|
def __init__(self, loss='deviance', learning_rate=0.1, n_estimators=100,
|
|
subsample=1.0, min_samples_split=2, min_samples_leaf=1,
|
|
max_depth=3, init=None, random_state=None,
|
|
max_features=None, verbose=0):
|
|
|
|
super(GradientBoostingClassifier, self).__init__(
|
|
loss, learning_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.
|
|
|
|
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.
|
|
"""
|
|
y = column_or_1d(y, warn=True)
|
|
self.classes_, y = unique(y, return_inverse=True)
|
|
self.n_classes_ = len(self.classes_)
|
|
|
|
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(score)
|
|
|
|
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):
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yield self.classes_.take(np.argmax(proba, axis=1), axis=0)
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class GradientBoostingRegressor(BaseGradientBoosting, RegressorMixin):
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"""Gradient Boosting for regression.
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GB builds an additive model in a forward stage-wise fashion;
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it allows for the optimization of arbitrary differentiable loss functions.
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In each stage a regression tree is fit on the negative gradient of the
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given loss function.
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|
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|
Parameters
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|
----------
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loss : {'ls', 'lad', 'huber', 'quantile'}, optional (default='ls')
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loss function to be optimized. 'ls' refers to least squares
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|
regression. 'lad' (least absolute deviation) is a highly robust
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|
loss function solely based on order information of the input
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variables. 'huber' is a combination of the two. 'quantile'
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|
allows quantile regression (use `alpha` to specify the quantile).
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|
|
|
learning_rate : float, optional (default=0.1)
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learning rate shrinks the contribution of each tree by `learning_rate`.
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There is a trade-off between learning_rate and n_estimators.
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|
|
|
n_estimators : int (default=100)
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The number of boosting stages to perform. Gradient boosting
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|
is fairly robust to over-fitting so a large number usually
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|
results in better performance.
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|
|
|
max_depth : integer, optional (default=3)
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|
maximum depth of the individual regression estimators. The maximum
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|
depth limits the number of nodes in the tree. Tune this parameter
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|
for best performance; the best value depends on the interaction
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|
of the input variables.
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|
|
|
min_samples_split : integer, optional (default=2)
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|
The minimum number of samples required to split an internal node.
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|
|
|
min_samples_leaf : integer, optional (default=1)
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|
The minimum number of samples required to be at a leaf node.
|
|
|
|
subsample : float, optional (default=1.0)
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|
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`.
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|
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
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|
`int(max_features * n_features)` features are considered at each
|
|
split.
|
|
- If "auto", then `max_features=n_features`.
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|
- If "sqrt", then `max_features=sqrt(n_features)`.
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|
- 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.
|
|
|
|
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.
|
|
|
|
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.
|
|
|
|
`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.
|
|
Deprecated: use `oob_improvement_` instead.
|
|
|
|
`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_`: list of DecisionTreeRegressor
|
|
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,
|
|
max_depth=3, init=None, random_state=None,
|
|
max_features=None, alpha=0.9, verbose=0):
|
|
|
|
super(GradientBoostingRegressor, self).__init__(
|
|
loss, learning_rate, n_estimators, min_samples_split,
|
|
min_samples_leaf, max_depth, init, subsample, max_features,
|
|
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.
|
|
|
|
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()
|