"""RobustWeightedEstimator meta estimator."""
# Author: Timothee Mathieu
# License: BSD 3 clause
import numpy as np
import warnings
from scipy.stats import iqr
from sklearn.base import (
BaseEstimator,
clone,
ClassifierMixin,
RegressorMixin,
ClusterMixin,
)
from sklearn.utils import (
check_random_state,
check_array,
check_consistent_length,
)
from sklearn.utils.validation import check_is_fitted
from sklearn.linear_model import SGDRegressor, SGDClassifier
from sklearn.multiclass import OneVsRestClassifier, OneVsOneClassifier
from sklearn.cluster import MiniBatchKMeans
from sklearn.metrics.pairwise import euclidean_distances
from sklearn.exceptions import ConvergenceWarning
from sklearn.utils.metaestimators import if_delegate_has_method
# Tool library in which we get robust mean estimators.
from .mean_estimators import median_of_means_blocked, block_mom, huber
from ._robust_weighted_estimator_helper import _kmeans_loss
# cython implementation of loss functions, copied from scikit-learn with light
# modifications.
from ._robust_weighted_estimator_helper import (
_kmeans_loss,
Log,
SquaredLoss,
Hinge,
Huber,
ModifiedHuber,
SquaredHinge,
)
LOSS_FUNCTIONS = {
"hinge": (Hinge,),
"log": (Log,),
"squared_error": (SquaredLoss,),
"squared_loss": (SquaredLoss,),
"squared_hinge": (SquaredHinge,),
"modified_huber": (ModifiedHuber,),
"huber": (Huber, 1.35), # 1.35 is default value. TODO : set as parameter
}
# Test version of sklearn, in version older than v1.0 squared_loss must be used
import sklearn
if sklearn.__version__[0] == "0":
SQ_LOSS = "squared_loss"
else:
SQ_LOSS = "squared_error"
def _huber_psisx(x, c):
"""Huber-loss weight for RobustWeightedEstimator algorithm"""
res = np.zeros(len(x))
res[np.abs(x) <= c] = 1
res[np.abs(x) > c] = c / np.abs(x)[np.abs(x) > c]
res[~np.isfinite(x)] = 0
return res
def _mom_psisx(med_block, n):
"""MOM weight for RobustWeightedEstimator algorithm"""
res = np.zeros(n)
res[med_block] = 1
return res
class _RobustWeightedEstimator(BaseEstimator):
"""Meta algorithm for robust regression and binary classification.
This model uses iterative reweighting of samples to make a regression or
classification estimator robust.
The principle of the algorithm is to use an empirical risk minimization
principle where the risk is estimated using a robust estimator (for example
Huber estimator or median-of-means estimator)[1], [3]. The idea behind this
algorithm was mentioned before in [2].
This idea translates in an iterative algorithm where the sample_weight
are changed at each iterations and are dependent of the sample. Informally
the outliers should have small weight while the inliers should have big
weight, where outliers are sample with a big loss function.
This algorithm enjoy a non-zero breakdown-point (it can handle arbitrarily
bad outliers). When the "mom" weighting scheme is used, k outliers can be
tolerated. When the "Huber" weighting scheme is used, asymptotically the
number of outliers has to be less than half the sample size.
Read more in the :ref:`User Guide <robust>`.
Parameters
----------
base_estimator : object, mandatory
The base estimator to fit. For now only SGDRegressor and SGDClassifier
are supported.
If None, then the base estimator is SGDRegressor with squared loss.
loss : string or callable, mandatory
Name of the loss used, must be the same loss as the one optimized in
base_estimator.
Classification losses supported : 'log', 'hinge', 'squared_hinge',
'modified_huber'. If 'log', then the base_estimator must support
predict_proba. Regression losses supported : 'squared_error', 'huber'.
If callable, the function is used as loss function ro construct
the weights.
weighting : string, default="huber"
Weighting scheme used to make the estimator robust.
Can be 'huber' for huber-type weights or 'mom' for median-of-means
type weights.
max_iter : int, default=100
Maximum number of iterations.
For more information, see the optimization scheme of base_estimator.
c : float>0 or None, default=None
Parameter used for Huber weighting procedure, used only if weightings
is 'huber'. Measure the robustness of the weighting procedure. A small
value of c means a more robust estimator.
Can have a big effect on efficiency.
If None, c is estimated at each step using half the Inter-quartile
range, this tends to be conservative (robust).
k : int < sample_size/2, default=1
Parameter used for mom weighting procedure, used only if weightings
is 'mom'. 2k+1 is the number of blocks used for median-of-means
estimation, higher value of k means a more robust estimator.
Can have a big effect on efficiency.
If None, k is estimated using the number of points distant from the
median of means of more than 2 times a robust estimate of the scale
(using the inter-quartile range), this tends to be conservative
(robust).
tol : float or None, (default = 1e-3)
The stopping criterion. If it is not None, training will stop when
(loss > best_loss - tol) for n_iter_no_change consecutive epochs.
n_iter_no_change : int, default=10
Number of iterations with no improvement to wait before early stopping.
verbose: int, default=0
If >0 will display the (robust) estimated loss every 10 epochs.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. 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_ : object,
The fitted base_estimator.
weights_ : array like, length = n_sample.
Weight of each sample at the end of the algorithm. Can be used as a
measure of how much of an outlier a sample is.
Notes
-----
For now only scikit-learn SGDRegressor and SGDClassifier are officially
supported but one can use any estimator compatible with scikit-learn,
as long as this estimator support partial_fit, warm_start and sample_weight
. It must have the parameters max_iter.
For now, only binary classification is implemented. See sklearn.multiclass
if you want to use this algorithm in multiclass classification.
References
----------
[1] Guillaume Lecué, Matthieu Lerasle and Timothée Mathieu.
"Robust classification via MOM minimization", arXiv preprint (2018).
arXiv:1808.03106
[2] Christian Brownlees, Emilien Joly and Gábor Lugosi.
"Empirical risk minimization for heavy-tailed losses", Ann. Statist.
Volume 43, Number 6 (2015), 2507-2536.
[3] Stanislav Minsker and Timothée Mathieu.
"Excess risk bounds in robust empirical risk minimization"
arXiv preprint (2019). arXiv:1910.07485.
"""
def __init__(
self,
base_estimator,
loss,
weighting="huber",
max_iter=100,
c=None,
k=0,
tol=1e-5,
n_iter_no_change=10,
verbose=0,
random_state=None,
):
self.base_estimator = base_estimator
self.weighting = weighting
self.c = c
self.k = k
self.loss = loss
self.max_iter = max_iter
self.tol = tol
self.n_iter_no_change = n_iter_no_change
self.verbose = verbose
self.random_state = random_state
def fit(self, X, y=None):
"""Fit the model to data matrix X and target(s) y.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
The input data.
y : array-like, shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels in classification, real numbers in
regression).
Returns
-------
self : returns an estimator trained with RobustWeightedEstimator.
"""
X = check_array(X)
if y is not None:
y = check_array(y, ensure_2d=False)
check_consistent_length(X, y)
random_state = check_random_state(self.random_state)
self._validate_hyperparameters(len(X))
# Initialization of all parameters in the base_estimator.
base_estimator = clone(self.base_estimator)
loss_param = self.loss
# Get actual loss function from its name.
loss = self._get_loss_function(loss_param)
parameters = list(base_estimator.get_params().keys())
if "warm_start" in parameters:
base_estimator.set_params(warm_start=True)
if ("loss" in parameters) and (loss_param != "squared_error"):
base_estimator.set_params(loss=loss_param)
if "n_iter_no_change" in parameters:
base_estimator.set_params(n_iter_no_change=self.n_iter_no_change)
base_estimator.set_params(random_state=random_state)
# Initialization
if self._estimator_type == "classifier":
classes = np.unique(y)
if len(classes) > 2:
raise ValueError("y must be binary.")
# Initialization of the estimator.
# Partial fit for the estimator to be set to "fitted" to be able
# to predict.
base_estimator.partial_fit(X, y, classes=classes)
# As the partial fit is here non-robust, override the
# learned coefs.
base_estimator.coef_ = np.zeros([1, len(X[0])])
base_estimator.intercept_ = np.array([0])
self.classes_ = base_estimator.classes_
elif self._estimator_type == "regressor":
# Initialization of the estimator
# Partial fit for the estimator to be set to "fitted" to be able
# to predict.
base_estimator.partial_fit(X, y)
# As the partial fit is here non-robust, override the
# learned coefs.
base_estimator.coef_ = np.zeros([len(X[0])])
base_estimator.intercept_ = np.array([0])
elif self._estimator_type == "clusterer":
# Partial fit for the estimator to be set to "fitted" to be able
# to predict.
base_estimator.partial_fit(X, y)
# Initialization of final weights
final_weights = np.zeros(len(X))
best_loss = np.inf
n_iter_no_change_ = 0
# Optimization algorithm
for epoch in range(self.max_iter):
if self._estimator_type == "classifier":
# If in classification, use decision_function
pred = base_estimator.decision_function(X)
else:
pred = base_estimator.predict(X)
# Compute the loss of each sample
if self._estimator_type == "clusterer":
loss_values = loss(X, pred)
elif self._estimator_type == "classifier":
# For classifiers, set the labels to {-1,1} for compatibility.
loss_values = loss(2 * y.flatten() - 1, pred)
else:
loss_values = loss(y.flatten(), pred)
# Compute the weight associated with each losses.
# Samples whose loss is far from the mean loss (robust estimation)
# will have a small weight.
weights, current_loss = self._get_weights(
loss_values, random_state
)
if (self.verbose > 0) and (epoch % 10 == 0):
print("Epoch ", epoch, " loss: %.2F" % (current_loss))
# Use the optimization algorithm of self.base_estimator for one
# epoch using the previously computed weights. Also shuffle the data.
perm = random_state.permutation(len(X))
base_estimator.partial_fit(X, y, sample_weight=weights)
if (self.tol is not None) and (
current_loss > best_loss - self.tol
):
n_iter_no_change_ += 1
else:
n_iter_no_change_ = 0
if current_loss < best_loss:
best_loss = current_loss
if n_iter_no_change_ == self.n_iter_no_change:
break
# Shuffle the data at each step.
if self._estimator_type == "clusterer":
# Here y is None
base_estimator.partial_fit(
X[perm], y, sample_weight=weights[perm]
)
else:
base_estimator.partial_fit(
X[perm], y[perm], sample_weight=weights[perm]
)
if (self.tol is not None) and (
current_loss > best_loss - self.tol
):
n_iter_no_change_ += 1
else:
n_iter_no_change_ = 0
if current_loss < best_loss:
best_loss = current_loss
if n_iter_no_change_ == self.n_iter_no_change:
break
elif epoch == self.max_iter - 1:
warnings.warn(
"Maximum number of iteration reached before "
"convergence. Consider increasing max_iter to "
"improve the fit.",
ConvergenceWarning,
)
if self.weighting == "mom":
final_weights += weights
if self.weighting == "mom":
self.weights_ = final_weights / self.max_iter
else:
self.weights_ = weights
self.base_estimator_ = base_estimator
self.n_iter_ = self.max_iter * len(X)
if hasattr(base_estimator, "coef_"):
self.coef_ = base_estimator.coef_
self.intercept_ = base_estimator.intercept_
if hasattr(base_estimator, "labels_"):
self.labels_ = self.base_estimator_.labels_
if hasattr(base_estimator, "cluster_centers_"):
self.cluster_centers_ = self.base_estimator_.cluster_centers_
self.inertia_ = self.base_estimator_.inertia_
return self
def _get_loss_function(self, loss):
"""Get concrete ''LossFunction'' object for str ''loss''."""
if type(loss) == str:
eff_loss = LOSS_FUNCTIONS.get(loss)
if eff_loss is None:
raise ValueError("The loss %s is not supported. " % self.loss)
loss_class, args = eff_loss[0], eff_loss[1:]
return np.vectorize(getattr(loss_class(*args), "py_loss"))
else:
return loss
def _validate_hyperparameters(self, n):
# Check the hyperparameters.
if self.max_iter <= 0:
raise ValueError("max_iter must be > 0, got %s." % self.max_iter)
if not (self.c is None) and (self.c <= 0):
raise ValueError("c must be > 0, got %s." % self.c)
if not (self.k is None) and (
not isinstance(self.k, int)
or self.k < 0
or self.k > np.floor(n / 2)
):
raise ValueError(
"k must be integer >= 0, and smaller than floor(sample_size/2)"
" got %s." % self.k
)
def _get_weights(self, loss_values, random_state):
# Compute the robust weight of the samples.
if self.weighting == "huber":
if self.c is None:
# If no c parameter given, estimate using inter quartile range.
c = iqr(loss_values) / 2
if c == 0:
warnings.warn(
"Too many samples are parfectly predicted "
"according to the loss function. "
"Switching to constant c = 1.35. "
"Consider using another weighting scheme, "
"or using a constant c value to remove "
"this warning."
)
c = 1.35
else:
c = self.c
def psisx(x):
return _huber_psisx(x, c)
# Robust estimation of the risk is in mu.
mu = huber(loss_values, c)
elif self.weighting == "mom":
if self.k is None:
med = np.median(loss_values)
# scale estimator using iqr, rescaled by what would be if the
# loss was Gaussian.
scale = iqr(np.abs(loss_values - med)) / 1.37
k = np.sum(np.abs(loss_values - med) > 2 * scale)
else:
k = self.k
# Choose (randomly) 2k+1 (almost-)equal blocks of data.
blocks = block_mom(loss_values, k, random_state)
# Compute the median-of-means of the losses using these blocks.
# Return also the index at which this median-of-means is attained.
mu, idmom = median_of_means_blocked(loss_values, blocks)
def psisx(x):
return _mom_psisx(blocks[idmom], len(loss_values))
else:
raise ValueError("No such weighting scheme")
# Compute the unnormalized weights.
w = psisx(loss_values - mu)
if self._estimator_type == "regressor":
return w / np.sum(w) * len(w), mu
else:
return w / np.sum(w), mu
def predict(self, X):
"""Predict using the estimator trained with RobustWeightedEstimator.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
y : array-like, shape (n_samples, n_outputs)
The predicted values.
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.predict(X)
def _check_proba(self):
if self.loss != "log":
raise AttributeError(
"Probability estimates are not available for"
" loss=%r" % self.loss
)
@property
def predict_proba(self):
check_is_fitted(self, attributes=["base_estimator_"])
self._check_proba()
return self._predict_proba
def _predict_proba(self, X):
return self.base_estimator_.predict_proba(X)
@property
def _estimator_type(self):
return self.base_estimator._estimator_type
def score(self, X, y=None):
"""Returns the score on the given data, using
``base_estimator_.score``.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Input data, where n_samples is the number of samples and
n_features is the number of features.
y : array-like of shape (n_samples, n_output) or (n_samples,), optional
Target relative to X for classification or regression;
None for unsupervised learning.
Returns
-------
score : float
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.score(X, y)
@if_delegate_has_method(delegate="base_estimator")
def decision_function(self, X):
"""Predict using the linear model. For classifiers only.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Returns
-------
array, shape (n_samples,)
Predicted target values per element in X.
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.decision_function(X)
[docs]class RobustWeightedClassifier(BaseEstimator, ClassifierMixin):
"""Algorithm for robust classification using reweighting algorithm.
This model uses iterative reweighting of samples to make a regression or
classification estimator robust.
The principle of the algorithm is to use an empirical risk minimization
principle where the risk is estimated using a robust estimator (for example
Huber estimator or median-of-means estimator)[1], [3]. The idea behind this
algorithm was mentioned before in [2].
This idea translates in an iterative algorithm where the sample_weight
are changed at each iterations and are dependent of the sample. Informally
the outliers should have small weight while the inliers should have big
weight, where outliers are sample with a big loss function.
This algorithm enjoy a non-zero breakdown-point (it can handle arbitrarily
bad outliers). When the "mom" weighting scheme is used, k outliers can be
tolerated. When the "Huber" weighting scheme is used, asymptotically the
number of outliers has to be less than half the sample size.
Read more in the :ref:`User Guide <robust>`.
Parameters
----------
weighting : string, default="huber"
Weighting scheme used to make the estimator robust.
Can be 'huber' for huber-type weights or 'mom' for median-of-means
type weights.
max_iter : int, default=100
Maximum number of iterations.
For more information, see the optimization scheme of base_estimator.
c : float>0 or None, default=None
Parameter used for Huber weighting procedure, used only if weightings
is 'huber'. Measure the robustness of the weighting procedure. A small
value of c means a more robust estimator.
Can have a big effect on efficiency.
If None, c is estimated at each step using half the Inter-quartile
range, this tends to be conservative (robust).
k : int < sample_size/2, default=1
Parameter used for mom weighting procedure, used only if weightings
is 'mom'. 2k+1 is the number of blocks used for median-of-means
estimation, higher value of k means a more robust estimator.
Can have a big effect on efficiency.
If None, k is estimated using the number of points distant from the
median of means of more than 2 times a robust estimate of the scale
(using the inter-quartile range), this tends to be conservative
(robust).
loss : string, None or callable, default="log"
Classification losses supported : 'log', 'hinge', 'modified_huber'.
If 'log', then the base_estimator must support predict_proba.
sgd_args : dict, default={}
arguments of the SGDClassifier base estimator.
multi_class : string, default="ovr"
multi-class scheme. Can be either "ovo" for OneVsOneClassifier or "ovr"
for OneVsRestClassifier or "binary" for binary classification.
n_jobs : int, default=1
number of jobs used in the multi-class meta-algorithm computation.
tol : float or None, (default = 1e-3)
The stopping criterion. If it is not None, training will stop when
(loss > best_loss - tol) for n_iter_no_change consecutive epochs.
n_iter_no_change : int, default=10
Number of iterations with no improvement to wait before early stopping.
verbose: int, default=0
If >0 will display the (robust) estimated loss every 10 epochs.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. 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
----------
classes_ : ndarray of shape (n_classes, )
A list of class labels known to the classifier.
coef_ : ndarray of shape (1, n_features) or (n_classes, n_features)
Coefficient of the features in the decision function. Only available if
multi_class = "binary"
intercept_ : ndarray of shape (1,) or (n_classes,)
Intercept (a.k.a. bias) added to the decision function.
Only available if multi_class = "binary"
n_iter_ : ndarray of shape (n_classes,) or (1, )
Actual number of iterations for all classes. If binary or multinomial,
it returns only 1 element. For liblinear solver, only the maximum
number of iteration across all classes is given.
base_estimator_ : object,
The fitted base estimator SGDCLassifier.
weights_ : array like, length = n_sample.
Weight of each sample at the end of the algorithm. Can be used as a
measure of how much of an outlier a sample is. Only available if
multi_class = "binary"
Notes
-----
Often, there is a need to use RobustScaler as preprocessing.
Examples
--------
>>> from sklearn_extra.robust import RobustWeightedClassifier
>>> from sklearn.datasets import make_blobs
>>> import numpy as np
>>> rng = np.random.RandomState(42)
>>> X,y = make_blobs(n_samples=100, centers=np.array([[-1, -1], [1, 1]]),
... random_state=rng)
>>> clf=RobustWeightedClassifier()
>>> _ = clf.fit(X, y)
>>> score = np.mean(clf.predict(X)==y)
References
----------
[1] Guillaume Lecué, Matthieu Lerasle and Timothée Mathieu.
"Robust classification via MOM minimization", Mach Learn 109, (2020).
https://doi.org/10.1007/s10994-019-05863-6 (2018).
arXiv:1808.03106
[2] Christian Brownlees, Emilien Joly and Gábor Lugosi.
"Empirical risk minimization for heavy-tailed losses", Ann. Statist.
Volume 43, Number 6 (2015), 2507-2536.
[3] Stanislav Minsker and Timothée Mathieu.
"Excess risk bounds in robust empirical risk minimization"
arXiv preprint (2019). arXiv:1910.07485.
"""
[docs] def __init__(
self,
weighting="huber",
max_iter=100,
c=None,
k=0,
loss="log",
sgd_args=None,
multi_class="ovr",
n_jobs=1,
tol=1e-3,
n_iter_no_change=10,
verbose=0,
random_state=None,
):
self.weighting = weighting
self.max_iter = max_iter
self.c = c
self.k = k
self.loss = loss
self.sgd_args = sgd_args
self.multi_class = multi_class
self.n_jobs = n_jobs
self.tol = tol
self.n_iter_no_change = n_iter_no_change
self.verbose = verbose
self.random_state = random_state
def fit(self, X, y):
"""Fit the model to data matrix X and target(s) y.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
The input data.
y : array-like, shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels in classification, real numbers in
regression).
Returns
-------
self : returns an estimator trained with RobustWeightedClassifier.
"""
if self.sgd_args is None:
sgd_args = {}
else:
sgd_args = self.sgd_args
# Define the base estimator
X, y = self._validate_data(X, y, y_numeric=False)
base_robust_estimator_ = _RobustWeightedEstimator(
SGDClassifier(**sgd_args),
weighting=self.weighting,
loss=self.loss,
c=self.c,
k=self.k,
max_iter=self.max_iter,
tol=self.tol,
n_iter_no_change=self.n_iter_no_change,
verbose=self.verbose,
random_state=self.random_state,
)
if self.multi_class == "ovr":
self.base_estimator_ = OneVsRestClassifier(
base_robust_estimator_, n_jobs=self.n_jobs
)
elif self.multi_class == "binary":
self.base_estimator_ = base_robust_estimator_
elif self.multi_class == "ovo":
self.base_estimator_ = OneVsOneClassifier(
base_robust_estimator_, n_jobs=self.n_jobs
)
else:
raise ValueError("No such multiclass method implemented.")
self.base_estimator_.fit(X, y)
if self.multi_class == "binary":
self.weights_ = self.base_estimator_.weights_
self.coef_ = self.base_estimator_.coef_
self.intercept_ = self.base_estimator_.intercept_
self.n_iter_ = self.max_iter * len(X)
self.classes_ = self.base_estimator_.classes_
return self
def predict(self, X):
"""Predict using the estimator trained with RobustWeightedClassifier.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
y : array-like, shape (n_samples, n_outputs)
The predicted values.
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.predict(X)
def _check_proba(self):
if self.loss != "log":
raise AttributeError(
"Probability estimates are not available for"
" loss=%r" % self.loss
)
@property
def predict_proba(self):
"""
Probability estimates when binary classification.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Vector to be scored, where `n_samples` is the number of samples and
`n_features` is the number of features.
Returns
-------
T : array-like of shape (n_samples, n_classes)
Returns the probability of the sample for each class in the model,
"""
check_is_fitted(self, attributes=["base_estimator_"])
self._check_proba()
return self._predict_proba
def _predict_proba(self, X):
return self.base_estimator_.predict_proba(X)
def score(self, X, y=None):
"""Returns the score on the given data, using
``base_estimator_.score``.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Input data, where n_samples is the number of samples and
n_features is the number of features.
y : array-like of shape (n_samples, n_output) or (n_samples,), optional
Target relative to X for classification or regression;
None for unsupervised learning.
Returns
-------
score : float
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.score(X, y)
def decision_function(self, X):
"""Predict using the linear model
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
Returns
-------
array, shape (n_samples,)
Predicted target values per element in X.
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.decision_function(X)
[docs]class RobustWeightedRegressor(BaseEstimator, RegressorMixin):
"""Algorithm for robust regression using reweighting algorithm.
This model uses iterative reweighting of samples to make a regression or
classification estimator robust.
The principle of the algorithm is to use an empirical risk minimization
principle where the risk is estimated using a robust estimator (for example
Huber estimator or median-of-means estimator)[1], [3]. The idea behind this
algorithm was mentioned before in [2].
This idea translates in an iterative algorithm where the sample_weight
are changed at each iterations and are dependent of the sample. Informally
the outliers should have small weight while the inliers should have big
weight, where outliers are sample with a big loss function.
This algorithm enjoy a non-zero breakdown-point (it can handle arbitrarily
bad outliers). When the "mom" weighting scheme is used, k outliers can be
tolerated. When the "Huber" weighting scheme is used, asymptotically the
number of outliers has to be less than half the sample size.
Read more in the :ref:`User Guide <robust>`.
Parameters
----------
weighting : string, default="huber"
Weighting scheme used to make the estimator robust.
Can be 'huber' for huber-type weights or 'mom' for median-of-means
type weights.
max_iter : int, default=100
Maximum number of iterations.
For more information, see the optimization scheme of base_estimator.
c : float>0 or None, default=None
Parameter used for Huber weighting procedure, used only if weightings
is 'huber'. Measure the robustness of the weighting procedure. A small
value of c means a more robust estimator.
Can have a big effect on efficiency.
If None, c is estimated at each step using half the Inter-quartile
range, this tends to be conservative (robust).
k : int < sample_size/2, default=1
Parameter used for mom weighting procedure, used only if weightings
is 'mom'. 2k+1 is the number of blocks used for median-of-means
estimation, higher value of k means a more robust estimator.
Can have a big effect on efficiency.
If None, k is estimated using the number of points distant from the
median of means of more than 2 times a robust estimate of the scale
(using the inter-quartile range), this tends to be conservative
(robust).
loss : string, None or callable, default="squared_error"
For now, only "squared_error" and "huber" are implemented.
sgd_args : dict, default={}
arguments of the SGDClassifier base estimator.
tol : float or None, (default = 1e-3)
The stopping criterion. If it is not None, training will stop when
(loss > best_loss - tol) for n_iter_no_change consecutive epochs.
n_iter_no_change : int, default=10
Number of iterations with no improvement to wait before early stopping.
verbose: int, default=0
If >0 will display the (robust) estimated loss every 10 epochs.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. 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
----------
coef_ : ndarray of shape (1, n_features) or (n_classes, n_features)
Coefficient of the features.
intercept_ : ndarray of shape (1,) or (n_classes,)
Intercept (a.k.a. bias).
n_iter_ : ndarray of shape (n_classes,) or (1, )
Actual number of iterations.
base_estimator_ : object,
The fitted base_estimator.
weights_ : array like, length = n_sample.
Weight of each sample at the end of the algorithm. Can be used as a
measure of how much of an outlier a sample is.
Notes
-----
Often, there is a need to use RobustScaler as preprocessing.
Examples
--------
>>> from sklearn_extra.robust import RobustWeightedRegressor
>>> from sklearn.datasets import make_regression
>>> import numpy as np
>>> rng = np.random.RandomState(42)
>>> X, y = make_regression()
>>> reg = RobustWeightedRegressor()
>>> _ = reg.fit(X, y)
>>> score = np.mean(reg.predict(X)==y)
References
----------
[1] Guillaume Lecué, Matthieu Lerasle and Timothée Mathieu.
"Robust classification via MOM minimization", Mach Learn 109, (2020).
https://doi.org/10.1007/s10994-019-05863-6 (2018).
arXiv:1808.03106
[2] Christian Brownlees, Emilien Joly and Gábor Lugosi.
"Empirical risk minimization for heavy-tailed losses", Ann. Statist.
Volume 43, Number 6 (2015), 2507-2536.
[3] Stanislav Minsker and Timothée Mathieu.
"Excess risk bounds in robust empirical risk minimization"
arXiv preprint (2019). arXiv:1910.07485.
"""
[docs] def __init__(
self,
weighting="huber",
max_iter=100,
c=None,
k=0,
loss=SQ_LOSS,
sgd_args=None,
tol=1e-3,
n_iter_no_change=10,
verbose=0,
random_state=None,
):
self.weighting = weighting
self.max_iter = max_iter
self.c = c
self.k = k
self.loss = loss
self.sgd_args = sgd_args
self.tol = tol
self.n_iter_no_change = n_iter_no_change
self.verbose = verbose
self.random_state = random_state
def fit(self, X, y):
"""Fit the model to data matrix X and target(s) y.
Parameters
----------
X : array-like or sparse matrix, shape (n_samples, n_features)
The input data.
y : array-like, shape (n_samples,) or (n_samples, n_outputs)
The target values (class labels in classification, real numbers in
regression).
Returns
-------
self : returns an estimator trained with RobustWeightedClassifier.
"""
if self.sgd_args is None:
sgd_args = {}
else:
sgd_args = self.sgd_args
# Define the base estimator
X, y = self._validate_data(X, y, y_numeric=True)
self.base_estimator_ = _RobustWeightedEstimator(
SGDRegressor(**sgd_args),
weighting=self.weighting,
loss=self.loss,
c=self.c,
k=self.k,
max_iter=self.max_iter,
tol=self.tol,
n_iter_no_change=self.n_iter_no_change,
verbose=self.verbose,
random_state=self.random_state,
)
self.base_estimator_.fit(X, y)
self.weights_ = self.base_estimator_.weights_
self.n_iter_ = self.max_iter * len(X)
self.coef_ = self.base_estimator_.coef_
self.intercept_ = self.base_estimator_.intercept_
return self
def predict(self, X):
"""Predict using the estimator trained with RobustWeightedRegressor.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
y : array-like, shape (n_samples, n_outputs)
The predicted values.
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.predict(X)
def score(self, X, y=None):
"""Returns the score on the given data, using
``base_estimator_.score``.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Input data, where n_samples is the number of samples and
n_features is the number of features.
y : array-like of shape (n_samples, n_output) or (n_samples,), optional
Target relative to X for classification or regression;
None for unsupervised learning.
Returns
-------
score : float
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.score(X, y)
[docs]class RobustWeightedKMeans(BaseEstimator, ClusterMixin):
"""Algorithm for robust kmeans clustering using reweighting algorithm.
This model uses iterative reweighting of samples to make a regression or
classification estimator robust.
The principle of the algorithm is to use an empirical risk minimization
principle where the risk is estimated using a robust estimator (for example
Huber estimator or median-of-means estimator)[1], [3]. The idea behind this
algorithm was mentioned before in [2].
This idea translates in an iterative algorithm where the sample_weight
are changed at each iterations and are dependent of the sample. Informally
the outliers should have small weight while the inliers should have big
weight, where outliers are sample with a big loss function.
This algorithm enjoy a non-zero breakdown-point (it can handle arbitrarily
bad outliers). When the "mom" weighting scheme is used, k outliers can be
tolerated. When the "Huber" weighting scheme is used, asymptotically the
number of outliers has to be less than half the sample size.
Read more in the :ref:`User Guide <robust>`.
Parameters
----------
weighting : string, default="huber"
Weighting scheme used to make the estimator robust.
Can be 'huber' for huber-type weights or 'mom' for median-of-means
type weights.
max_iter : int, default=100
Maximum number of iterations.
For more information, see the optimization scheme of base_estimator.
c : float>0 or None, default=None
Parameter used for Huber weighting procedure, used only if weightings
is 'huber'. Measure the robustness of the weighting procedure. A small
value of c means a more robust estimator.
Can have a big effect on efficiency.
If None, c is estimated at each step using half the Inter-quartile
range, this tends to be conservative (robust).
k : int < sample_size/2, default=1
Parameter used for mom weighting procedure, used only if weightings
is 'mom'. 2k+1 is the number of blocks used for median-of-means
estimation, higher value of k means a more robust estimator.
Can have a big effect on efficiency.
If None, k is estimated using the number of points distant from the
median of means of more than 2 times a robust estimate of the scale
(using the inter-quartile range), this tends to be conservative
(robust).
kmeans_args : dict, default={}
arguments of the MiniBatchKMeans base estimator. Must not contain
batch_size.
tol : float or None, (default = 1e-3)
The stopping criterion. If it is not None, training will stop when
(loss > best_loss - tol) for n_iter_no_change consecutive epochs.
n_iter_no_change : int, default=10
Number of iterations with no improvement to wait before early stopping.
verbose: int, default=0
If >0 will display the (robust) estimated loss every 10 epochs.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. 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
----------
cluster_centers_ : ndarray of shape (n_clusters, n_features)
Coordinates of cluster centers. If the algorithm stops before fully
converging (see ``tol`` and ``max_iter``), these will not be
consistent with ``labels_``.
labels_ : ndarray of shape (n_samples,)
Labels of each point
inertia_ : float
Sum of squared distances of samples to their closest cluster center.
n_iter_ : int
Number of iterations run.
base_estimator_ : object,
The fitted base_estimator.
weights_ : array like, length = n_sample.
Weight of each sample at the end of the algorithm. Can be used as a
measure of how much of an outlier a sample is.
Notes
-----
One may need to use RobustScaler as a preprocessing.
Examples
--------
>>> from sklearn_extra.robust import RobustWeightedKMeans
>>> from sklearn.datasets import make_blobs
>>> import numpy as np
>>> rng = np.random.RandomState(42)
>>> X,y = make_blobs(n_samples=100, centers=np.array([[-1, -1], [1, 1]]),
... random_state=rng)
>>> km = RobustWeightedKMeans()
>>> _ = km.fit(X)
>>> score = np.mean((km.predict(X)-y)**2)
References
----------
[1] Guillaume Lecué, Matthieu Lerasle and Timothée Mathieu.
"Robust classification via MOM minimization", Mach Learn 109, (2020).
https://doi.org/10.1007/s10994-019-05863-6 (2018).
arXiv:1808.03106
[2] Christian Brownlees, Emilien Joly and Gábor Lugosi.
"Empirical risk minimization for heavy-tailed losses", Ann. Statist.
Volume 43, Number 6 (2015), 2507-2536.
[3] Stanislav Minsker and Timothée Mathieu.
"Excess risk bounds in robust empirical risk minimization"
arXiv preprint (2019). arXiv:1910.07485.
"""
[docs] def __init__(
self,
n_clusters=8,
weighting="huber",
max_iter=100,
c=None,
k=0,
kmeans_args=None,
tol=1e-3,
n_iter_no_change=10,
verbose=0,
random_state=None,
):
self.n_clusters = n_clusters
self.weighting = weighting
self.max_iter = max_iter
self.c = c
self.k = k
self.kmeans_args = kmeans_args
self.tol = tol
self.n_iter_no_change = n_iter_no_change
self.verbose = verbose
self.random_state = random_state
def fit(self, X, y=None):
"""Compute k-means clustering.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
Training instances to cluster.
y : Ignored
Not used, present here for API consistency by convention.
Returns
-------
self
Fitted estimator.
"""
if self.kmeans_args is None:
kmeans_args = {}
else:
kmeans_args = self.kmeans_args
X = self._validate_data(
X,
accept_sparse="csr",
dtype=[np.float64, np.float32],
order="C",
accept_large_sparse=False,
)
self.base_estimator_ = _RobustWeightedEstimator(
MiniBatchKMeans(
self.n_clusters,
batch_size=X.shape[0],
random_state=self.random_state,
**kmeans_args
),
weighting=self.weighting,
loss=_kmeans_loss,
max_iter=self.max_iter,
c=self.c,
k=self.k,
tol=self.tol,
n_iter_no_change=self.n_iter_no_change,
verbose=self.verbose,
random_state=self.random_state,
)
self.base_estimator_.fit(X)
self.cluster_centers_ = self.base_estimator_.cluster_centers_
self.n_iter_ = self.max_iter * len(X)
self.labels_ = self.predict(X)
self.inertia_ = self.base_estimator_.inertia_
self.weights_ = self.base_estimator_.weights_
return self
def predict(self, X):
"""Predict using the estimator trained with RobustWeightedClassifier.
Parameters
----------
X : {array-like, sparse matrix}, shape (n_samples, n_features)
The input data.
Returns
-------
y : array-like, shape (n_samples, n_outputs)
The predicted values.
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.predict(X)
def score(self, X, y=None):
"""Returns the score on the given data, using
``base_estimator_.score``.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Input data, where n_samples is the number of samples and
n_features is the number of features.
y : array-like of shape (n_samples, n_output) or (n_samples,), optional
Target relative to X for classification or regression;
None for unsupervised learning.
Returns
-------
score : float
"""
check_is_fitted(self, attributes=["base_estimator_"])
return self.base_estimator_.score(X, y)
def transform(self, X):
"""Transform X to a cluster-distance space.
In the new space, each dimension is the distance to the cluster
centers. Note that even if X is sparse, the array returned by
`transform` will typically be dense.
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_features)
New data to transform.
Returns
-------
X_new : ndarray of shape (n_samples, n_clusters)
X transformed in the new space.
"""
check_is_fitted(self)
return self._transform(X)
def _transform(self, X):
"""guts of transform method; no input validation"""
return euclidean_distances(X, self.cluster_centers_)
def fit_transform(self, X, y=None):
return self.fit(X)._transform(X)