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/ ensemble / _weight_boosting.py
"""Weight Boosting
This module contains weight boosting estimators for both classification and
regression.
The module structure is the following:
- The ``BaseWeightBoosting`` base class implements a common ``fit`` method
for all the estimators in the module. Regression and classification
only differ from each other in the loss function that is optimized.
- ``AdaBoostClassifier`` implements adaptive boosting (AdaBoost-SAMME) for
classification problems.
- ``AdaBoostRegressor`` implements adaptive boosting (AdaBoost.R2) for
regression problems.
"""
# Authors: Noel Dawe <noel@dawe.me>
# Gilles Louppe <g.louppe@gmail.com>
# Hamzeh Alsalhi <ha258@cornell.edu>
# Arnaud Joly <arnaud.v.joly@gmail.com>
#
# License: BSD 3 clause
from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.special import xlogy
from ._base import BaseEnsemble
from ..base import ClassifierMixin, RegressorMixin, is_classifier, is_regressor
from ..tree import DecisionTreeClassifier, DecisionTreeRegressor
from ..utils import check_array, check_random_state, check_X_y, _safe_indexing
from ..utils.extmath import softmax
from ..utils.extmath import stable_cumsum
from ..metrics import accuracy_score, r2_score
from ..utils.validation import check_is_fitted
from ..utils.validation import _check_sample_weight
from ..utils.validation import has_fit_parameter
from ..utils.validation import _num_samples
__all__ = [
'AdaBoostClassifier',
'AdaBoostRegressor',
]
class BaseWeightBoosting(BaseEnsemble, metaclass=ABCMeta):
"""Base class for AdaBoost estimators.
Warning: This class should not be used directly. Use derived classes
instead.
"""
@abstractmethod
def __init__(self,
base_estimator=None,
n_estimators=50,
estimator_params=tuple(),
learning_rate=1.,
random_state=None):
super().__init__(
base_estimator=base_estimator,
n_estimators=n_estimators,
estimator_params=estimator_params)
self.learning_rate = learning_rate
self.random_state = random_state
def _validate_data(self, X, y=None):
# Accept or convert to these sparse matrix formats so we can
# use _safe_indexing
accept_sparse = ['csr', 'csc']
if y is None:
ret = check_array(X,
accept_sparse=accept_sparse,
ensure_2d=False,
allow_nd=True,
dtype=None)
else:
ret = check_X_y(X, y,
accept_sparse=accept_sparse,
ensure_2d=False,
allow_nd=True,
dtype=None,
y_numeric=is_regressor(self))
return ret
def fit(self, X, y, sample_weight=None):
"""Build a boosted classifier/regressor from the training set (X, y).
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
y : array-like of shape (n_samples,)
The target values (class labels in classification, real numbers in
regression).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, the sample weights are initialized to
1 / n_samples.
Returns
-------
self : object
"""
# Check parameters
if self.learning_rate <= 0:
raise ValueError("learning_rate must be greater than zero")
X, y = self._validate_data(X, y)
sample_weight = _check_sample_weight(sample_weight, X, np.float64)
sample_weight /= sample_weight.sum()
if np.any(sample_weight < 0):
raise ValueError("sample_weight cannot contain negative weights")
# Check parameters
self._validate_estimator()
# Clear any previous fit results
self.estimators_ = []
self.estimator_weights_ = np.zeros(self.n_estimators, dtype=np.float64)
self.estimator_errors_ = np.ones(self.n_estimators, dtype=np.float64)
random_state = check_random_state(self.random_state)
for iboost in range(self.n_estimators):
# Boosting step
sample_weight, estimator_weight, estimator_error = self._boost(
iboost,
X, y,
sample_weight,
random_state)
# Early termination
if sample_weight is None:
break
self.estimator_weights_[iboost] = estimator_weight
self.estimator_errors_[iboost] = estimator_error
# Stop if error is zero
if estimator_error == 0:
break
sample_weight_sum = np.sum(sample_weight)
# Stop if the sum of sample weights has become non-positive
if sample_weight_sum <= 0:
break
if iboost < self.n_estimators - 1:
# Normalize
sample_weight /= sample_weight_sum
return self
@abstractmethod
def _boost(self, iboost, X, y, sample_weight, random_state):
"""Implement a single boost.
Warning: This method needs to be overridden by subclasses.
Parameters
----------
iboost : int
The index of the current boost iteration.
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
y : array-like of shape (n_samples,)
The target values (class labels).
sample_weight : array-like of shape (n_samples,)
The current sample weights.
random_state : RandomState
The current random number generator
Returns
-------
sample_weight : array-like of shape (n_samples,) or None
The reweighted sample weights.
If None then boosting has terminated early.
estimator_weight : float
The weight for the current boost.
If None then boosting has terminated early.
error : float
The classification error for the current boost.
If None then boosting has terminated early.
"""
pass
def staged_score(self, X, y, sample_weight=None):
"""Return staged scores for X, y.
This generator method yields the ensemble score after each iteration of
boosting and therefore allows monitoring, such as to determine the
score on a test set after each boost.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
y : array-like of shape (n_samples,)
Labels for X.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Yields
------
z : float
"""
X = self._validate_data(X)
for y_pred in self.staged_predict(X):
if is_classifier(self):
yield accuracy_score(y, y_pred, sample_weight=sample_weight)
else:
yield r2_score(y, y_pred, sample_weight=sample_weight)
@property
def feature_importances_(self):
"""Return the feature importances (the higher, the more important the
feature).
Returns
-------
feature_importances_ : ndarray of shape (n_features,)
The feature importances.
"""
if self.estimators_ is None or len(self.estimators_) == 0:
raise ValueError("Estimator not fitted, "
"call `fit` before `feature_importances_`.")
try:
norm = self.estimator_weights_.sum()
return (sum(weight * clf.feature_importances_ for weight, clf
in zip(self.estimator_weights_, self.estimators_))
/ norm)
except AttributeError:
raise AttributeError(
"Unable to compute feature importances "
"since base_estimator does not have a "
"feature_importances_ attribute")
def _samme_proba(estimator, n_classes, X):
"""Calculate algorithm 4, step 2, equation c) of Zhu et al [1].
References
----------
.. [1] J. Zhu, H. Zou, S. Rosset, T. Hastie, "Multi-class AdaBoost", 2009.
"""
proba = estimator.predict_proba(X)
# Displace zero probabilities so the log is defined.
# Also fix negative elements which may occur with
# negative sample weights.
np.clip(proba, np.finfo(proba.dtype).eps, None, out=proba)
log_proba = np.log(proba)
return (n_classes - 1) * (log_proba - (1. / n_classes)
* log_proba.sum(axis=1)[:, np.newaxis])
class AdaBoostClassifier(ClassifierMixin, BaseWeightBoosting):
"""An AdaBoost classifier.
An AdaBoost [1] classifier is a meta-estimator that begins by fitting a
classifier on the original dataset and then fits additional copies of the
classifier on the same dataset but where the weights of incorrectly
classified instances are adjusted such that subsequent classifiers focus
more on difficult cases.
This class implements the algorithm known as AdaBoost-SAMME [2].
Read more in the :ref:`User Guide <adaboost>`.
.. versionadded:: 0.14
Parameters
----------
base_estimator : object, optional (default=None)
The base estimator from which the boosted ensemble is built.
Support for sample weighting is required, as well as proper
``classes_`` and ``n_classes_`` attributes. If ``None``, then
the base estimator is ``DecisionTreeClassifier(max_depth=1)``.
n_estimators : int, optional (default=50)
The maximum number of estimators at which boosting is terminated.
In case of perfect fit, the learning procedure is stopped early.
learning_rate : float, optional (default=1.)
Learning rate shrinks the contribution of each classifier by
``learning_rate``. There is a trade-off between ``learning_rate`` and
``n_estimators``.
algorithm : {'SAMME', 'SAMME.R'}, optional (default='SAMME.R')
If 'SAMME.R' then use the SAMME.R real boosting algorithm.
``base_estimator`` must support calculation of class probabilities.
If 'SAMME' then use the SAMME discrete boosting algorithm.
The SAMME.R algorithm typically converges faster than SAMME,
achieving a lower test error with fewer boosting iterations.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
Attributes
----------
base_estimator_ : estimator
The base estimator from which the ensemble is grown.
estimators_ : list of classifiers
The collection of fitted sub-estimators.
classes_ : array of shape (n_classes,)
The classes labels.
n_classes_ : int
The number of classes.
estimator_weights_ : array of floats
Weights for each estimator in the boosted ensemble.
estimator_errors_ : array of floats
Classification error for each estimator in the boosted
ensemble.
feature_importances_ : ndarray of shape (n_features,)
The feature importances if supported by the ``base_estimator``.
See Also
--------
AdaBoostRegressor
An AdaBoost regressor that begins by fitting a regressor on the
original dataset and then fits additional copies of the regressor
on the same dataset but where the weights of instances are
adjusted according to the error of the current prediction.
GradientBoostingClassifier
GB builds an additive model in a forward stage-wise fashion. 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.
sklearn.tree.DecisionTreeClassifier
A non-parametric supervised learning method used for classification.
Creates a model that predicts the value of a target variable by
learning simple decision rules inferred from the data features.
References
----------
.. [1] Y. Freund, R. Schapire, "A Decision-Theoretic Generalization of
on-Line Learning and an Application to Boosting", 1995.
.. [2] J. Zhu, H. Zou, S. Rosset, T. Hastie, "Multi-class AdaBoost", 2009.
Examples
--------
>>> from sklearn.ensemble import AdaBoostClassifier
>>> from sklearn.datasets import make_classification
>>> X, y = make_classification(n_samples=1000, n_features=4,
... n_informative=2, n_redundant=0,
... random_state=0, shuffle=False)
>>> clf = AdaBoostClassifier(n_estimators=100, random_state=0)
>>> clf.fit(X, y)
AdaBoostClassifier(n_estimators=100, random_state=0)
>>> clf.feature_importances_
array([0.28..., 0.42..., 0.14..., 0.16...])
>>> clf.predict([[0, 0, 0, 0]])
array([1])
>>> clf.score(X, y)
0.983...
"""
def __init__(self,
base_estimator=None,
n_estimators=50,
learning_rate=1.,
algorithm='SAMME.R',
random_state=None):
super().__init__(
base_estimator=base_estimator,
n_estimators=n_estimators,
learning_rate=learning_rate,
random_state=random_state)
self.algorithm = algorithm
def fit(self, X, y, sample_weight=None):
"""Build a boosted classifier from the training set (X, y).
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
y : array-like of shape (n_samples,)
The target values (class labels).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, the sample weights are initialized to
``1 / n_samples``.
Returns
-------
self : object
Fitted estimator.
"""
# Check that algorithm is supported
if self.algorithm not in ('SAMME', 'SAMME.R'):
raise ValueError("algorithm %s is not supported" % self.algorithm)
# Fit
return super().fit(X, y, sample_weight)
def _validate_estimator(self):
"""Check the estimator and set the base_estimator_ attribute."""
super()._validate_estimator(
default=DecisionTreeClassifier(max_depth=1))
# SAMME-R requires predict_proba-enabled base estimators
if self.algorithm == 'SAMME.R':
if not hasattr(self.base_estimator_, 'predict_proba'):
raise TypeError(
"AdaBoostClassifier with algorithm='SAMME.R' requires "
"that the weak learner supports the calculation of class "
"probabilities with a predict_proba method.\n"
"Please change the base estimator or set "
"algorithm='SAMME' instead.")
if not has_fit_parameter(self.base_estimator_, "sample_weight"):
raise ValueError("%s doesn't support sample_weight."
% self.base_estimator_.__class__.__name__)
def _boost(self, iboost, X, y, sample_weight, random_state):
"""Implement a single boost.
Perform a single boost according to the real multi-class SAMME.R
algorithm or to the discrete SAMME algorithm and return the updated
sample weights.
Parameters
----------
iboost : int
The index of the current boost iteration.
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples.
y : array-like of shape (n_samples,)
The target values (class labels).
sample_weight : array-like of shape (n_samples,)
The current sample weights.
random_state : RandomState
The current random number generator
Returns
-------
sample_weight : array-like of shape (n_samples,) or None
The reweighted sample weights.
If None then boosting has terminated early.
estimator_weight : float
The weight for the current boost.
If None then boosting has terminated early.
estimator_error : float
The classification error for the current boost.
If None then boosting has terminated early.
"""
if self.algorithm == 'SAMME.R':
return self._boost_real(iboost, X, y, sample_weight, random_state)
else: # elif self.algorithm == "SAMME":
return self._boost_discrete(iboost, X, y, sample_weight,
random_state)
def _boost_real(self, iboost, X, y, sample_weight, random_state):
"""Implement a single boost using the SAMME.R real algorithm."""
estimator = self._make_estimator(random_state=random_state)
estimator.fit(X, y, sample_weight=sample_weight)
y_predict_proba = estimator.predict_proba(X)
if iboost == 0:
self.classes_ = getattr(estimator, 'classes_', None)
self.n_classes_ = len(self.classes_)
y_predict = self.classes_.take(np.argmax(y_predict_proba, axis=1),
axis=0)
# Instances incorrectly classified
incorrect = y_predict != y
# Error fraction
estimator_error = np.mean(
np.average(incorrect, weights=sample_weight, axis=0))
# Stop if classification is perfect
if estimator_error <= 0:
return sample_weight, 1., 0.
# Construct y coding as described in Zhu et al [2]:
#
# y_k = 1 if c == k else -1 / (K - 1)
#
# where K == n_classes_ and c, k in [0, K) are indices along the second
# axis of the y coding with c being the index corresponding to the true
# class label.
n_classes = self.n_classes_
classes = self.classes_
y_codes = np.array([-1. / (n_classes - 1), 1.])
y_coding = y_codes.take(classes == y[:, np.newaxis])
# Displace zero probabilities so the log is defined.
# Also fix negative elements which may occur with
# negative sample weights.
proba = y_predict_proba # alias for readability
np.clip(proba, np.finfo(proba.dtype).eps, None, out=proba)
# Boost weight using multi-class AdaBoost SAMME.R alg
estimator_weight = (-1. * self.learning_rate
* ((n_classes - 1.) / n_classes)
* xlogy(y_coding, y_predict_proba).sum(axis=1))
# Only boost the weights if it will fit again
if not iboost == self.n_estimators - 1:
# Only boost positive weights
sample_weight *= np.exp(estimator_weight *
((sample_weight > 0) |
(estimator_weight < 0)))
return sample_weight, 1., estimator_error
def _boost_discrete(self, iboost, X, y, sample_weight, random_state):
"""Implement a single boost using the SAMME discrete algorithm."""
estimator = self._make_estimator(random_state=random_state)
estimator.fit(X, y, sample_weight=sample_weight)
y_predict = estimator.predict(X)
if iboost == 0:
self.classes_ = getattr(estimator, 'classes_', None)
self.n_classes_ = len(self.classes_)
# Instances incorrectly classified
incorrect = y_predict != y
# Error fraction
estimator_error = np.mean(
np.average(incorrect, weights=sample_weight, axis=0))
# Stop if classification is perfect
if estimator_error <= 0:
return sample_weight, 1., 0.
n_classes = self.n_classes_
# Stop if the error is at least as bad as random guessing
if estimator_error >= 1. - (1. / n_classes):
self.estimators_.pop(-1)
if len(self.estimators_) == 0:
raise ValueError('BaseClassifier in AdaBoostClassifier '
'ensemble is worse than random, ensemble '
'can not be fit.')
return None, None, None
# Boost weight using multi-class AdaBoost SAMME alg
estimator_weight = self.learning_rate * (
np.log((1. - estimator_error) / estimator_error) +
np.log(n_classes - 1.))
# Only boost the weights if I will fit again
if not iboost == self.n_estimators - 1:
# Only boost positive weights
sample_weight *= np.exp(estimator_weight * incorrect *
(sample_weight > 0))
return sample_weight, estimator_weight, estimator_error
def predict(self, X):
"""Predict classes for X.
The predicted class of an input sample is computed as the weighted mean
prediction of the classifiers in the ensemble.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Returns
-------
y : ndarray of shape (n_samples,)
The predicted classes.
"""
X = self._validate_data(X)
pred = self.decision_function(X)
if self.n_classes_ == 2:
return self.classes_.take(pred > 0, axis=0)
return self.classes_.take(np.argmax(pred, axis=1), axis=0)
def staged_predict(self, X):
"""Return staged predictions for X.
The predicted class of an input sample is computed as the weighted mean
prediction of the classifiers in the ensemble.
This generator method yields the ensemble prediction after each
iteration of boosting and therefore allows monitoring, such as to
determine the prediction on a test set after each boost.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Yields
------
y : generator of array, shape = [n_samples]
The predicted classes.
"""
X = self._validate_data(X)
n_classes = self.n_classes_
classes = self.classes_
if n_classes == 2:
for pred in self.staged_decision_function(X):
yield np.array(classes.take(pred > 0, axis=0))
else:
for pred in self.staged_decision_function(X):
yield np.array(classes.take(
np.argmax(pred, axis=1), axis=0))
def decision_function(self, X):
"""Compute the decision function of ``X``.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Returns
-------
score : array, shape = [n_samples, k]
The decision function of the input samples. The order of
outputs is the same of that of the :term:`classes_` attribute.
Binary classification is a special cases with ``k == 1``,
otherwise ``k==n_classes``. For binary classification,
values closer to -1 or 1 mean more like the first or second
class in ``classes_``, respectively.
"""
check_is_fitted(self)
X = self._validate_data(X)
n_classes = self.n_classes_
classes = self.classes_[:, np.newaxis]
if self.algorithm == 'SAMME.R':
# The weights are all 1. for SAMME.R
pred = sum(_samme_proba(estimator, n_classes, X)
for estimator in self.estimators_)
else: # self.algorithm == "SAMME"
pred = sum((estimator.predict(X) == classes).T * w
for estimator, w in zip(self.estimators_,
self.estimator_weights_))
pred /= self.estimator_weights_.sum()
if n_classes == 2:
pred[:, 0] *= -1
return pred.sum(axis=1)
return pred
def staged_decision_function(self, X):
"""Compute decision function of ``X`` for each boosting iteration.
This method allows monitoring (i.e. determine error on testing set)
after each boosting iteration.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Yields
------
score : generator of array, shape = [n_samples, k]
The decision function of the input samples. The order of
outputs is the same of that of the :term:`classes_` attribute.
Binary classification is a special cases with ``k == 1``,
otherwise ``k==n_classes``. For binary classification,
values closer to -1 or 1 mean more like the first or second
class in ``classes_``, respectively.
"""
check_is_fitted(self)
X = self._validate_data(X)
n_classes = self.n_classes_
classes = self.classes_[:, np.newaxis]
pred = None
norm = 0.
for weight, estimator in zip(self.estimator_weights_,
self.estimators_):
norm += weight
if self.algorithm == 'SAMME.R':
# The weights are all 1. for SAMME.R
current_pred = _samme_proba(estimator, n_classes, X)
else: # elif self.algorithm == "SAMME":
current_pred = estimator.predict(X)
current_pred = (current_pred == classes).T * weight
if pred is None:
pred = current_pred
else:
pred += current_pred
if n_classes == 2:
tmp_pred = np.copy(pred)
tmp_pred[:, 0] *= -1
yield (tmp_pred / norm).sum(axis=1)
else:
yield pred / norm
@staticmethod
def _compute_proba_from_decision(decision, n_classes):
"""Compute probabilities from the decision function.
This is based eq. (4) of [1] where:
p(y=c|X) = exp((1 / K-1) f_c(X)) / sum_k(exp((1 / K-1) f_k(X)))
= softmax((1 / K-1) * f(X))
References
----------
.. [1] J. Zhu, H. Zou, S. Rosset, T. Hastie, "Multi-class AdaBoost",
2009.
"""
if n_classes == 2:
decision = np.vstack([-decision, decision]).T / 2
else:
decision /= (n_classes - 1)
return softmax(decision, copy=False)
def predict_proba(self, X):
"""Predict class probabilities for X.
The predicted class probabilities of an input sample is computed as
the weighted mean predicted class probabilities of the classifiers
in the ensemble.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Returns
-------
p : array of shape (n_samples, n_classes)
The class probabilities of the input samples. The order of
outputs is the same of that of the :term:`classes_` attribute.
"""
check_is_fitted(self)
X = self._validate_data(X)
n_classes = self.n_classes_
if n_classes == 1:
return np.ones((_num_samples(X), 1))
decision = self.decision_function(X)
return self._compute_proba_from_decision(decision, n_classes)
def staged_predict_proba(self, X):
"""Predict class probabilities for X.
The predicted class probabilities of an input sample is computed as
the weighted mean predicted class probabilities of the classifiers
in the ensemble.
This generator method yields the ensemble predicted class probabilities
after each iteration of boosting and therefore allows monitoring, such
as to determine the predicted class probabilities on a test set after
each boost.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Yields
-------
p : generator of array, shape = [n_samples]
The class probabilities of the input samples. The order of
outputs is the same of that of the :term:`classes_` attribute.
"""
X = self._validate_data(X)
n_classes = self.n_classes_
for decision in self.staged_decision_function(X):
yield self._compute_proba_from_decision(decision, n_classes)
def predict_log_proba(self, X):
"""Predict class log-probabilities for X.
The predicted class log-probabilities of an input sample is computed as
the weighted mean predicted class log-probabilities of the classifiers
in the ensemble.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Returns
-------
p : array of shape (n_samples, n_classes)
The class probabilities of the input samples. The order of
outputs is the same of that of the :term:`classes_` attribute.
"""
X = self._validate_data(X)
return np.log(self.predict_proba(X))
class AdaBoostRegressor(RegressorMixin, BaseWeightBoosting):
"""An AdaBoost regressor.
An AdaBoost [1] regressor is a meta-estimator that begins by fitting a
regressor on the original dataset and then fits additional copies of the
regressor on the same dataset but where the weights of instances are
adjusted according to the error of the current prediction. As such,
subsequent regressors focus more on difficult cases.
This class implements the algorithm known as AdaBoost.R2 [2].
Read more in the :ref:`User Guide <adaboost>`.
.. versionadded:: 0.14
Parameters
----------
base_estimator : object, optional (default=None)
The base estimator from which the boosted ensemble is built.
If ``None``, then the base estimator is
``DecisionTreeRegressor(max_depth=3)``.
n_estimators : integer, optional (default=50)
The maximum number of estimators at which boosting is terminated.
In case of perfect fit, the learning procedure is stopped early.
learning_rate : float, optional (default=1.)
Learning rate shrinks the contribution of each regressor by
``learning_rate``. There is a trade-off between ``learning_rate`` and
``n_estimators``.
loss : {'linear', 'square', 'exponential'}, optional (default='linear')
The loss function to use when updating the weights after each
boosting iteration.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator;
If RandomState instance, random_state is the random number generator;
If None, the random number generator is the RandomState instance used
by `np.random`.
Attributes
----------
base_estimator_ : estimator
The base estimator from which the ensemble is grown.
estimators_ : list of classifiers
The collection of fitted sub-estimators.
estimator_weights_ : array of floats
Weights for each estimator in the boosted ensemble.
estimator_errors_ : array of floats
Regression error for each estimator in the boosted ensemble.
feature_importances_ : ndarray of shape (n_features,)
The feature importances if supported by the ``base_estimator``.
Examples
--------
>>> from sklearn.ensemble import AdaBoostRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=4, n_informative=2,
... random_state=0, shuffle=False)
>>> regr = AdaBoostRegressor(random_state=0, n_estimators=100)
>>> regr.fit(X, y)
AdaBoostRegressor(n_estimators=100, random_state=0)
>>> regr.feature_importances_
array([0.2788..., 0.7109..., 0.0065..., 0.0036...])
>>> regr.predict([[0, 0, 0, 0]])
array([4.7972...])
>>> regr.score(X, y)
0.9771...
See also
--------
AdaBoostClassifier, GradientBoostingRegressor,
sklearn.tree.DecisionTreeRegressor
References
----------
.. [1] Y. Freund, R. Schapire, "A Decision-Theoretic Generalization of
on-Line Learning and an Application to Boosting", 1995.
.. [2] H. Drucker, "Improving Regressors using Boosting Techniques", 1997.
"""
def __init__(self,
base_estimator=None,
n_estimators=50,
learning_rate=1.,
loss='linear',
random_state=None):
super().__init__(
base_estimator=base_estimator,
n_estimators=n_estimators,
learning_rate=learning_rate,
random_state=random_state)
self.loss = loss
self.random_state = random_state
def fit(self, X, y, sample_weight=None):
"""Build a boosted regressor from the training set (X, y).
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
y : array-like of shape (n_samples,)
The target values (real numbers).
sample_weight : array-like of shape (n_samples,), default=None
Sample weights. If None, the sample weights are initialized to
1 / n_samples.
Returns
-------
self : object
"""
# Check loss
if self.loss not in ('linear', 'square', 'exponential'):
raise ValueError(
"loss must be 'linear', 'square', or 'exponential'")
# Fit
return super().fit(X, y, sample_weight)
def _validate_estimator(self):
"""Check the estimator and set the base_estimator_ attribute."""
super()._validate_estimator(
default=DecisionTreeRegressor(max_depth=3))
def _boost(self, iboost, X, y, sample_weight, random_state):
"""Implement a single boost for regression
Perform a single boost according to the AdaBoost.R2 algorithm and
return the updated sample weights.
Parameters
----------
iboost : int
The index of the current boost iteration.
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples.
y : array-like of shape (n_samples,)
The target values (class labels in classification, real numbers in
regression).
sample_weight : array-like of shape (n_samples,)
The current sample weights.
random_state : RandomState
The current random number generator
Returns
-------
sample_weight : array-like of shape (n_samples,) or None
The reweighted sample weights.
If None then boosting has terminated early.
estimator_weight : float
The weight for the current boost.
If None then boosting has terminated early.
estimator_error : float
The regression error for the current boost.
If None then boosting has terminated early.
"""
estimator = self._make_estimator(random_state=random_state)
# Weighted sampling of the training set with replacement
bootstrap_idx = random_state.choice(
np.arange(_num_samples(X)), size=_num_samples(X), replace=True,
p=sample_weight
)
# Fit on the bootstrapped sample and obtain a prediction
# for all samples in the training set
X_ = _safe_indexing(X, bootstrap_idx)
y_ = _safe_indexing(y, bootstrap_idx)
estimator.fit(X_, y_)
y_predict = estimator.predict(X)
error_vect = np.abs(y_predict - y)
sample_mask = sample_weight > 0
masked_sample_weight = sample_weight[sample_mask]
masked_error_vector = error_vect[sample_mask]
error_max = masked_error_vector.max()
if error_max != 0:
masked_error_vector /= error_max
if self.loss == 'square':
masked_error_vector **= 2
elif self.loss == 'exponential':
masked_error_vector = 1. - np.exp(-masked_error_vector)
# Calculate the average loss
estimator_error = (masked_sample_weight * masked_error_vector).sum()
if estimator_error <= 0:
# Stop if fit is perfect
return sample_weight, 1., 0.
elif estimator_error >= 0.5:
# Discard current estimator only if it isn't the only one
if len(self.estimators_) > 1:
self.estimators_.pop(-1)
return None, None, None
beta = estimator_error / (1. - estimator_error)
# Boost weight using AdaBoost.R2 alg
estimator_weight = self.learning_rate * np.log(1. / beta)
if not iboost == self.n_estimators - 1:
sample_weight[sample_mask] *= np.power(
beta, (1. - masked_error_vector) * self.learning_rate
)
return sample_weight, estimator_weight, estimator_error
def _get_median_predict(self, X, limit):
# Evaluate predictions of all estimators
predictions = np.array([
est.predict(X) for est in self.estimators_[:limit]]).T
# Sort the predictions
sorted_idx = np.argsort(predictions, axis=1)
# Find index of median prediction for each sample
weight_cdf = stable_cumsum(self.estimator_weights_[sorted_idx], axis=1)
median_or_above = weight_cdf >= 0.5 * weight_cdf[:, -1][:, np.newaxis]
median_idx = median_or_above.argmax(axis=1)
median_estimators = sorted_idx[np.arange(_num_samples(X)), median_idx]
# Return median predictions
return predictions[np.arange(_num_samples(X)), median_estimators]
def predict(self, X):
"""Predict regression value for X.
The predicted regression value of an input sample is computed
as the weighted median prediction of the classifiers in the ensemble.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples. Sparse matrix can be CSC, CSR, COO,
DOK, or LIL. COO, DOK, and LIL are converted to CSR.
Returns
-------
y : ndarray of shape (n_samples,)
The predicted regression values.
"""
check_is_fitted(self)
X = self._validate_data(X)
return self._get_median_predict(X, len(self.estimators_))
def staged_predict(self, X):
"""Return staged predictions for X.
The predicted regression value of an input sample is computed
as the weighted median prediction of the classifiers in the ensemble.
This generator method yields the ensemble prediction after each
iteration of boosting and therefore allows monitoring, such as to
determine the prediction on a test set after each boost.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
The training input samples.
Yields
-------
y : generator of array, shape = [n_samples]
The predicted regression values.
"""
check_is_fitted(self)
X = self._validate_data(X)
for i, _ in enumerate(self.estimators_, 1):
yield self._get_median_predict(X, limit=i)