1000 lines
31 KiB
Python
1000 lines
31 KiB
Python
"""Losses and corresponding default initial estimators for gradient boosting
|
|
decision trees.
|
|
"""
|
|
|
|
from abc import ABCMeta
|
|
from abc import abstractmethod
|
|
|
|
import numpy as np
|
|
from scipy.special import expit, logsumexp
|
|
|
|
from ..tree._tree import TREE_LEAF
|
|
from ..utils.stats import _weighted_percentile
|
|
from ..dummy import DummyClassifier
|
|
from ..dummy import DummyRegressor
|
|
|
|
|
|
class LossFunction(metaclass=ABCMeta):
|
|
"""Abstract base class for various loss functions.
|
|
|
|
Parameters
|
|
----------
|
|
n_classes : int
|
|
Number of classes.
|
|
|
|
Attributes
|
|
----------
|
|
K : int
|
|
The number of regression trees to be induced;
|
|
1 for regression and binary classification;
|
|
``n_classes`` for multi-class classification.
|
|
"""
|
|
|
|
is_multi_class = False
|
|
|
|
def __init__(self, n_classes):
|
|
self.K = n_classes
|
|
|
|
@abstractmethod
|
|
def init_estimator(self):
|
|
"""Default ``init`` estimator for loss function."""
|
|
|
|
@abstractmethod
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the loss.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves).
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
|
|
@abstractmethod
|
|
def negative_gradient(self, y, raw_predictions, **kargs):
|
|
"""Compute the negative gradient.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
"""
|
|
|
|
def update_terminal_regions(
|
|
self,
|
|
tree,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
sample_mask,
|
|
learning_rate=0.1,
|
|
k=0,
|
|
):
|
|
"""Update the terminal regions (=leaves) of the given tree and
|
|
updates the current predictions of the model. Traverses tree
|
|
and invokes template method `_update_terminal_region`.
|
|
|
|
Parameters
|
|
----------
|
|
tree : tree.Tree
|
|
The tree object.
|
|
X : ndarray of shape (n_samples, n_features)
|
|
The data array.
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
residual : ndarray of shape (n_samples,)
|
|
The residuals (usually the negative gradient).
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
sample_weight : ndarray of shape (n_samples,)
|
|
The weight of each sample.
|
|
sample_mask : ndarray of shape (n_samples,)
|
|
The sample mask to be used.
|
|
learning_rate : float, default=0.1
|
|
Learning rate shrinks the contribution of each tree by
|
|
``learning_rate``.
|
|
k : int, default=0
|
|
The index of the estimator being updated.
|
|
|
|
"""
|
|
# compute leaf for each sample in ``X``.
|
|
terminal_regions = tree.apply(X)
|
|
|
|
# mask all which are not in sample mask.
|
|
masked_terminal_regions = terminal_regions.copy()
|
|
masked_terminal_regions[~sample_mask] = -1
|
|
|
|
# update each leaf (= perform line search)
|
|
for leaf in np.where(tree.children_left == TREE_LEAF)[0]:
|
|
self._update_terminal_region(
|
|
tree,
|
|
masked_terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions[:, k],
|
|
sample_weight,
|
|
)
|
|
|
|
# update predictions (both in-bag and out-of-bag)
|
|
raw_predictions[:, k] += learning_rate * tree.value[:, 0, 0].take(
|
|
terminal_regions, axis=0
|
|
)
|
|
|
|
@abstractmethod
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
"""Template method for updating terminal regions (i.e., leaves)."""
|
|
|
|
@abstractmethod
|
|
def get_init_raw_predictions(self, X, estimator):
|
|
"""Return the initial raw predictions.
|
|
|
|
Parameters
|
|
----------
|
|
X : ndarray of shape (n_samples, n_features)
|
|
The data array.
|
|
estimator : object
|
|
The estimator to use to compute the predictions.
|
|
|
|
Returns
|
|
-------
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The initial raw predictions. K is equal to 1 for binary
|
|
classification and regression, and equal to the number of classes
|
|
for multiclass classification. ``raw_predictions`` is casted
|
|
into float64.
|
|
"""
|
|
pass
|
|
|
|
|
|
class RegressionLossFunction(LossFunction, metaclass=ABCMeta):
|
|
"""Base class for regression loss functions."""
|
|
|
|
def __init__(self):
|
|
super().__init__(n_classes=1)
|
|
|
|
def check_init_estimator(self, estimator):
|
|
"""Make sure estimator has the required fit and predict methods.
|
|
|
|
Parameters
|
|
----------
|
|
estimator : object
|
|
The init estimator to check.
|
|
"""
|
|
if not (hasattr(estimator, "fit") and hasattr(estimator, "predict")):
|
|
raise ValueError(
|
|
"The init parameter must be a valid estimator and "
|
|
"support both fit and predict."
|
|
)
|
|
|
|
def get_init_raw_predictions(self, X, estimator):
|
|
predictions = estimator.predict(X)
|
|
return predictions.reshape(-1, 1).astype(np.float64)
|
|
|
|
|
|
class LeastSquaresError(RegressionLossFunction):
|
|
"""Loss function for least squares (LS) estimation.
|
|
Terminal regions do not need to be updated for least squares.
|
|
|
|
Parameters
|
|
----------
|
|
n_classes : int
|
|
Number of classes.
|
|
"""
|
|
|
|
def init_estimator(self):
|
|
return DummyRegressor(strategy="mean")
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the least squares loss.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves).
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
if sample_weight is None:
|
|
return np.mean((y - raw_predictions.ravel()) ** 2)
|
|
else:
|
|
return (
|
|
1
|
|
/ sample_weight.sum()
|
|
* np.sum(sample_weight * ((y - raw_predictions.ravel()) ** 2))
|
|
)
|
|
|
|
def negative_gradient(self, y, raw_predictions, **kargs):
|
|
"""Compute half of the negative gradient.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples,)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
"""
|
|
return y - raw_predictions.ravel()
|
|
|
|
def update_terminal_regions(
|
|
self,
|
|
tree,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
sample_mask,
|
|
learning_rate=0.1,
|
|
k=0,
|
|
):
|
|
"""Least squares does not need to update terminal regions.
|
|
|
|
But it has to update the predictions.
|
|
|
|
Parameters
|
|
----------
|
|
tree : tree.Tree
|
|
The tree object.
|
|
X : ndarray of shape (n_samples, n_features)
|
|
The data array.
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
residual : ndarray of shape (n_samples,)
|
|
The residuals (usually the negative gradient).
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
sample_weight : ndarray of shape (n,)
|
|
The weight of each sample.
|
|
sample_mask : ndarray of shape (n,)
|
|
The sample mask to be used.
|
|
learning_rate : float, default=0.1
|
|
Learning rate shrinks the contribution of each tree by
|
|
``learning_rate``.
|
|
k : int, default=0
|
|
The index of the estimator being updated.
|
|
"""
|
|
# update predictions
|
|
raw_predictions[:, k] += learning_rate * tree.predict(X).ravel()
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
pass
|
|
|
|
|
|
class LeastAbsoluteError(RegressionLossFunction):
|
|
"""Loss function for least absolute deviation (LAD) regression.
|
|
|
|
Parameters
|
|
----------
|
|
n_classes : int
|
|
Number of classes
|
|
"""
|
|
|
|
def init_estimator(self):
|
|
return DummyRegressor(strategy="quantile", quantile=0.5)
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the least absolute error.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves).
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
if sample_weight is None:
|
|
return np.abs(y - raw_predictions.ravel()).mean()
|
|
else:
|
|
return (
|
|
1
|
|
/ sample_weight.sum()
|
|
* np.sum(sample_weight * np.abs(y - raw_predictions.ravel()))
|
|
)
|
|
|
|
def negative_gradient(self, y, raw_predictions, **kargs):
|
|
"""Compute the negative gradient.
|
|
|
|
1.0 if y - raw_predictions > 0.0 else -1.0
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
"""
|
|
raw_predictions = raw_predictions.ravel()
|
|
return 2 * (y - raw_predictions > 0) - 1
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
"""LAD updates terminal regions to median estimates."""
|
|
terminal_region = np.where(terminal_regions == leaf)[0]
|
|
sample_weight = sample_weight.take(terminal_region, axis=0)
|
|
diff = y.take(terminal_region, axis=0) - raw_predictions.take(
|
|
terminal_region, axis=0
|
|
)
|
|
tree.value[leaf, 0, 0] = _weighted_percentile(
|
|
diff, sample_weight, percentile=50
|
|
)
|
|
|
|
|
|
class HuberLossFunction(RegressionLossFunction):
|
|
"""Huber loss function for robust regression.
|
|
|
|
M-Regression proposed in Friedman 2001.
|
|
|
|
Parameters
|
|
----------
|
|
alpha : float, default=0.9
|
|
Percentile at which to extract score.
|
|
|
|
References
|
|
----------
|
|
J. Friedman, Greedy Function Approximation: A Gradient Boosting
|
|
Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.
|
|
"""
|
|
|
|
def __init__(self, alpha=0.9):
|
|
super().__init__()
|
|
self.alpha = alpha
|
|
self.gamma = None
|
|
|
|
def init_estimator(self):
|
|
return DummyRegressor(strategy="quantile", quantile=0.5)
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the Huber loss.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
raw_predictions = raw_predictions.ravel()
|
|
diff = y - raw_predictions
|
|
gamma = self.gamma
|
|
if gamma is None:
|
|
if sample_weight is None:
|
|
gamma = np.percentile(np.abs(diff), self.alpha * 100)
|
|
else:
|
|
gamma = _weighted_percentile(
|
|
np.abs(diff), sample_weight, self.alpha * 100
|
|
)
|
|
|
|
gamma_mask = np.abs(diff) <= gamma
|
|
if sample_weight is None:
|
|
sq_loss = np.sum(0.5 * diff[gamma_mask] ** 2)
|
|
lin_loss = np.sum(gamma * (np.abs(diff[~gamma_mask]) - gamma / 2))
|
|
loss = (sq_loss + lin_loss) / y.shape[0]
|
|
else:
|
|
sq_loss = np.sum(0.5 * sample_weight[gamma_mask] * diff[gamma_mask] ** 2)
|
|
lin_loss = np.sum(
|
|
gamma
|
|
* sample_weight[~gamma_mask]
|
|
* (np.abs(diff[~gamma_mask]) - gamma / 2)
|
|
)
|
|
loss = (sq_loss + lin_loss) / sample_weight.sum()
|
|
return loss
|
|
|
|
def negative_gradient(self, y, raw_predictions, sample_weight=None, **kargs):
|
|
"""Compute the negative gradient.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
raw_predictions = raw_predictions.ravel()
|
|
diff = y - raw_predictions
|
|
if sample_weight is None:
|
|
gamma = np.percentile(np.abs(diff), self.alpha * 100)
|
|
else:
|
|
gamma = _weighted_percentile(np.abs(diff), sample_weight, self.alpha * 100)
|
|
gamma_mask = np.abs(diff) <= gamma
|
|
residual = np.zeros((y.shape[0],), dtype=np.float64)
|
|
residual[gamma_mask] = diff[gamma_mask]
|
|
residual[~gamma_mask] = gamma * np.sign(diff[~gamma_mask])
|
|
self.gamma = gamma
|
|
return residual
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
terminal_region = np.where(terminal_regions == leaf)[0]
|
|
sample_weight = sample_weight.take(terminal_region, axis=0)
|
|
gamma = self.gamma
|
|
diff = y.take(terminal_region, axis=0) - raw_predictions.take(
|
|
terminal_region, axis=0
|
|
)
|
|
median = _weighted_percentile(diff, sample_weight, percentile=50)
|
|
diff_minus_median = diff - median
|
|
tree.value[leaf, 0] = median + np.mean(
|
|
np.sign(diff_minus_median) * np.minimum(np.abs(diff_minus_median), gamma)
|
|
)
|
|
|
|
|
|
class QuantileLossFunction(RegressionLossFunction):
|
|
"""Loss function for quantile regression.
|
|
|
|
Quantile regression allows to estimate the percentiles
|
|
of the conditional distribution of the target.
|
|
|
|
Parameters
|
|
----------
|
|
alpha : float, default=0.9
|
|
The percentile.
|
|
"""
|
|
|
|
def __init__(self, alpha=0.9):
|
|
super().__init__()
|
|
self.alpha = alpha
|
|
self.percentile = alpha * 100
|
|
|
|
def init_estimator(self):
|
|
return DummyRegressor(strategy="quantile", quantile=self.alpha)
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the Quantile loss.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
raw_predictions = raw_predictions.ravel()
|
|
diff = y - raw_predictions
|
|
alpha = self.alpha
|
|
|
|
mask = y > raw_predictions
|
|
if sample_weight is None:
|
|
loss = (
|
|
alpha * diff[mask].sum() - (1 - alpha) * diff[~mask].sum()
|
|
) / y.shape[0]
|
|
else:
|
|
loss = (
|
|
alpha * np.sum(sample_weight[mask] * diff[mask])
|
|
- (1 - alpha) * np.sum(sample_weight[~mask] * diff[~mask])
|
|
) / sample_weight.sum()
|
|
return loss
|
|
|
|
def negative_gradient(self, y, raw_predictions, **kargs):
|
|
"""Compute the negative gradient.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
"""
|
|
alpha = self.alpha
|
|
raw_predictions = raw_predictions.ravel()
|
|
mask = y > raw_predictions
|
|
return (alpha * mask) - ((1 - alpha) * ~mask)
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
terminal_region = np.where(terminal_regions == leaf)[0]
|
|
diff = y.take(terminal_region, axis=0) - raw_predictions.take(
|
|
terminal_region, axis=0
|
|
)
|
|
sample_weight = sample_weight.take(terminal_region, axis=0)
|
|
|
|
val = _weighted_percentile(diff, sample_weight, self.percentile)
|
|
tree.value[leaf, 0] = val
|
|
|
|
|
|
class ClassificationLossFunction(LossFunction, metaclass=ABCMeta):
|
|
"""Base class for classification loss functions."""
|
|
|
|
@abstractmethod
|
|
def _raw_prediction_to_proba(self, raw_predictions):
|
|
"""Template method to convert raw predictions into probabilities.
|
|
|
|
Parameters
|
|
----------
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
Returns
|
|
-------
|
|
probas : ndarray of shape (n_samples, K)
|
|
The predicted probabilities.
|
|
"""
|
|
|
|
@abstractmethod
|
|
def _raw_prediction_to_decision(self, raw_predictions):
|
|
"""Template method to convert raw predictions to decisions.
|
|
|
|
Parameters
|
|
----------
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
Returns
|
|
-------
|
|
encoded_predictions : ndarray of shape (n_samples, K)
|
|
The predicted encoded labels.
|
|
"""
|
|
|
|
def check_init_estimator(self, estimator):
|
|
"""Make sure estimator has fit and predict_proba methods.
|
|
|
|
Parameters
|
|
----------
|
|
estimator : object
|
|
The init estimator to check.
|
|
"""
|
|
if not (hasattr(estimator, "fit") and hasattr(estimator, "predict_proba")):
|
|
raise ValueError(
|
|
"The init parameter must be a valid estimator "
|
|
"and support both fit and predict_proba."
|
|
)
|
|
|
|
|
|
class BinomialDeviance(ClassificationLossFunction):
|
|
"""Binomial deviance loss function for binary classification.
|
|
|
|
Binary classification is a special case; here, we only need to
|
|
fit one tree instead of ``n_classes`` trees.
|
|
|
|
Parameters
|
|
----------
|
|
n_classes : int
|
|
Number of classes.
|
|
"""
|
|
|
|
def __init__(self, n_classes):
|
|
if n_classes != 2:
|
|
raise ValueError(
|
|
"{0:s} requires 2 classes; got {1:d} class(es)".format(
|
|
self.__class__.__name__, n_classes
|
|
)
|
|
)
|
|
# we only need to fit one tree for binary clf.
|
|
super().__init__(n_classes=1)
|
|
|
|
def init_estimator(self):
|
|
# return the most common class, taking into account the samples
|
|
# weights
|
|
return DummyClassifier(strategy="prior")
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the deviance (= 2 * negative log-likelihood).
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
# logaddexp(0, v) == log(1.0 + exp(v))
|
|
raw_predictions = raw_predictions.ravel()
|
|
if sample_weight is None:
|
|
return -2 * np.mean(
|
|
(y * raw_predictions) - np.logaddexp(0, raw_predictions)
|
|
)
|
|
else:
|
|
return (
|
|
-2
|
|
/ sample_weight.sum()
|
|
* np.sum(
|
|
sample_weight
|
|
* ((y * raw_predictions) - np.logaddexp(0, raw_predictions))
|
|
)
|
|
)
|
|
|
|
def negative_gradient(self, y, raw_predictions, **kargs):
|
|
"""Compute half of the negative gradient.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
"""
|
|
return y - expit(raw_predictions.ravel())
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
"""Make a single Newton-Raphson step.
|
|
|
|
our node estimate is given by:
|
|
|
|
sum(w * (y - prob)) / sum(w * prob * (1 - prob))
|
|
|
|
we take advantage that: y - prob = residual
|
|
"""
|
|
terminal_region = np.where(terminal_regions == leaf)[0]
|
|
residual = residual.take(terminal_region, axis=0)
|
|
y = y.take(terminal_region, axis=0)
|
|
sample_weight = sample_weight.take(terminal_region, axis=0)
|
|
|
|
numerator = np.sum(sample_weight * residual)
|
|
denominator = np.sum(sample_weight * (y - residual) * (1 - y + residual))
|
|
|
|
# prevents overflow and division by zero
|
|
if abs(denominator) < 1e-150:
|
|
tree.value[leaf, 0, 0] = 0.0
|
|
else:
|
|
tree.value[leaf, 0, 0] = numerator / denominator
|
|
|
|
def _raw_prediction_to_proba(self, raw_predictions):
|
|
proba = np.ones((raw_predictions.shape[0], 2), dtype=np.float64)
|
|
proba[:, 1] = expit(raw_predictions.ravel())
|
|
proba[:, 0] -= proba[:, 1]
|
|
return proba
|
|
|
|
def _raw_prediction_to_decision(self, raw_predictions):
|
|
proba = self._raw_prediction_to_proba(raw_predictions)
|
|
return np.argmax(proba, axis=1)
|
|
|
|
def get_init_raw_predictions(self, X, estimator):
|
|
probas = estimator.predict_proba(X)
|
|
proba_pos_class = probas[:, 1]
|
|
eps = np.finfo(np.float32).eps
|
|
proba_pos_class = np.clip(proba_pos_class, eps, 1 - eps)
|
|
# log(x / (1 - x)) is the inverse of the sigmoid (expit) function
|
|
raw_predictions = np.log(proba_pos_class / (1 - proba_pos_class))
|
|
return raw_predictions.reshape(-1, 1).astype(np.float64)
|
|
|
|
|
|
class MultinomialDeviance(ClassificationLossFunction):
|
|
"""Multinomial deviance loss function for multi-class classification.
|
|
|
|
For multi-class classification we need to fit ``n_classes`` trees at
|
|
each stage.
|
|
|
|
Parameters
|
|
----------
|
|
n_classes : int
|
|
Number of classes.
|
|
"""
|
|
|
|
is_multi_class = True
|
|
|
|
def __init__(self, n_classes):
|
|
if n_classes < 3:
|
|
raise ValueError(
|
|
"{0:s} requires more than 2 classes.".format(self.__class__.__name__)
|
|
)
|
|
super().__init__(n_classes)
|
|
|
|
def init_estimator(self):
|
|
return DummyClassifier(strategy="prior")
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the Multinomial deviance.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
# create one-hot label encoding
|
|
Y = np.zeros((y.shape[0], self.K), dtype=np.float64)
|
|
for k in range(self.K):
|
|
Y[:, k] = y == k
|
|
|
|
return np.average(
|
|
-1 * (Y * raw_predictions).sum(axis=1) + logsumexp(raw_predictions, axis=1),
|
|
weights=sample_weight,
|
|
)
|
|
|
|
def negative_gradient(self, y, raw_predictions, k=0, **kwargs):
|
|
"""Compute negative gradient for the ``k``-th class.
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
The target labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
|
|
k : int, default=0
|
|
The index of the class.
|
|
"""
|
|
return y - np.nan_to_num(
|
|
np.exp(raw_predictions[:, k] - logsumexp(raw_predictions, axis=1))
|
|
)
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
"""Make a single Newton-Raphson step."""
|
|
terminal_region = np.where(terminal_regions == leaf)[0]
|
|
residual = residual.take(terminal_region, axis=0)
|
|
y = y.take(terminal_region, axis=0)
|
|
sample_weight = sample_weight.take(terminal_region, axis=0)
|
|
|
|
numerator = np.sum(sample_weight * residual)
|
|
numerator *= (self.K - 1) / self.K
|
|
|
|
denominator = np.sum(sample_weight * (y - residual) * (1 - y + residual))
|
|
|
|
# prevents overflow and division by zero
|
|
if abs(denominator) < 1e-150:
|
|
tree.value[leaf, 0, 0] = 0.0
|
|
else:
|
|
tree.value[leaf, 0, 0] = numerator / denominator
|
|
|
|
def _raw_prediction_to_proba(self, raw_predictions):
|
|
return np.nan_to_num(
|
|
np.exp(
|
|
raw_predictions - (logsumexp(raw_predictions, axis=1)[:, np.newaxis])
|
|
)
|
|
)
|
|
|
|
def _raw_prediction_to_decision(self, raw_predictions):
|
|
proba = self._raw_prediction_to_proba(raw_predictions)
|
|
return np.argmax(proba, axis=1)
|
|
|
|
def get_init_raw_predictions(self, X, estimator):
|
|
probas = estimator.predict_proba(X)
|
|
eps = np.finfo(np.float32).eps
|
|
probas = np.clip(probas, eps, 1 - eps)
|
|
raw_predictions = np.log(probas).astype(np.float64)
|
|
return raw_predictions
|
|
|
|
|
|
class ExponentialLoss(ClassificationLossFunction):
|
|
"""Exponential loss function for binary classification.
|
|
|
|
Same loss as AdaBoost.
|
|
|
|
Parameters
|
|
----------
|
|
n_classes : int
|
|
Number of classes.
|
|
|
|
References
|
|
----------
|
|
Greg Ridgeway, Generalized Boosted Models: A guide to the gbm package, 2007
|
|
"""
|
|
|
|
def __init__(self, n_classes):
|
|
if n_classes != 2:
|
|
raise ValueError(
|
|
"{0:s} requires 2 classes; got {1:d} class(es)".format(
|
|
self.__class__.__name__, n_classes
|
|
)
|
|
)
|
|
# we only need to fit one tree for binary clf.
|
|
super().__init__(n_classes=1)
|
|
|
|
def init_estimator(self):
|
|
return DummyClassifier(strategy="prior")
|
|
|
|
def __call__(self, y, raw_predictions, sample_weight=None):
|
|
"""Compute the exponential loss
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble.
|
|
|
|
sample_weight : ndarray of shape (n_samples,), default=None
|
|
Sample weights.
|
|
"""
|
|
raw_predictions = raw_predictions.ravel()
|
|
if sample_weight is None:
|
|
return np.mean(np.exp(-(2.0 * y - 1.0) * raw_predictions))
|
|
else:
|
|
return (
|
|
1.0
|
|
/ sample_weight.sum()
|
|
* np.sum(sample_weight * np.exp(-(2 * y - 1) * raw_predictions))
|
|
)
|
|
|
|
def negative_gradient(self, y, raw_predictions, **kargs):
|
|
"""Compute the residual (= negative gradient).
|
|
|
|
Parameters
|
|
----------
|
|
y : ndarray of shape (n_samples,)
|
|
True labels.
|
|
|
|
raw_predictions : ndarray of shape (n_samples, K)
|
|
The raw predictions (i.e. values from the tree leaves) of the
|
|
tree ensemble at iteration ``i - 1``.
|
|
"""
|
|
y_ = 2.0 * y - 1.0
|
|
return y_ * np.exp(-y_ * raw_predictions.ravel())
|
|
|
|
def _update_terminal_region(
|
|
self,
|
|
tree,
|
|
terminal_regions,
|
|
leaf,
|
|
X,
|
|
y,
|
|
residual,
|
|
raw_predictions,
|
|
sample_weight,
|
|
):
|
|
terminal_region = np.where(terminal_regions == leaf)[0]
|
|
raw_predictions = raw_predictions.take(terminal_region, axis=0)
|
|
y = y.take(terminal_region, axis=0)
|
|
sample_weight = sample_weight.take(terminal_region, axis=0)
|
|
|
|
y_ = 2.0 * y - 1.0
|
|
|
|
numerator = np.sum(y_ * sample_weight * np.exp(-y_ * raw_predictions))
|
|
denominator = np.sum(sample_weight * np.exp(-y_ * raw_predictions))
|
|
|
|
# prevents overflow and division by zero
|
|
if abs(denominator) < 1e-150:
|
|
tree.value[leaf, 0, 0] = 0.0
|
|
else:
|
|
tree.value[leaf, 0, 0] = numerator / denominator
|
|
|
|
def _raw_prediction_to_proba(self, raw_predictions):
|
|
proba = np.ones((raw_predictions.shape[0], 2), dtype=np.float64)
|
|
proba[:, 1] = expit(2.0 * raw_predictions.ravel())
|
|
proba[:, 0] -= proba[:, 1]
|
|
return proba
|
|
|
|
def _raw_prediction_to_decision(self, raw_predictions):
|
|
return (raw_predictions.ravel() >= 0).astype(int)
|
|
|
|
def get_init_raw_predictions(self, X, estimator):
|
|
probas = estimator.predict_proba(X)
|
|
proba_pos_class = probas[:, 1]
|
|
eps = np.finfo(np.float32).eps
|
|
proba_pos_class = np.clip(proba_pos_class, eps, 1 - eps)
|
|
# according to The Elements of Statistical Learning sec. 10.5, the
|
|
# minimizer of the exponential loss is .5 * log odds ratio. So this is
|
|
# the equivalent to .5 * binomial_deviance.get_init_raw_predictions()
|
|
raw_predictions = 0.5 * np.log(proba_pos_class / (1 - proba_pos_class))
|
|
return raw_predictions.reshape(-1, 1).astype(np.float64)
|
|
|
|
|
|
LOSS_FUNCTIONS = {
|
|
"squared_error": LeastSquaresError,
|
|
"absolute_error": LeastAbsoluteError,
|
|
"huber": HuberLossFunction,
|
|
"quantile": QuantileLossFunction,
|
|
# TODO(1.3): Remove deviance
|
|
"deviance": None, # for both, multinomial and binomial
|
|
"log_loss": None, # for both, multinomial and binomial
|
|
"exponential": ExponentialLoss,
|
|
}
|