891 lines
31 KiB
Python
891 lines
31 KiB
Python
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"""Calibration of predicted probabilities."""
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# Author: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.fr>
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# Balazs Kegl <balazs.kegl@gmail.com>
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# Jan Hendrik Metzen <jhm@informatik.uni-bremen.de>
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# Mathieu Blondel <mathieu@mblondel.org>
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#
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# License: BSD 3 clause
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import warnings
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from inspect import signature
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from contextlib import suppress
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from functools import partial
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from math import log
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import numpy as np
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from joblib import Parallel
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from scipy.special import expit
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from scipy.special import xlogy
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from scipy.optimize import fmin_bfgs
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from .base import (BaseEstimator, ClassifierMixin, RegressorMixin, clone,
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MetaEstimatorMixin)
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from .preprocessing import label_binarize, LabelEncoder
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from .utils import (
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check_array,
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column_or_1d,
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deprecated,
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indexable,
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)
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from .utils.multiclass import check_classification_targets
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from .utils.fixes import delayed
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from .utils.validation import check_is_fitted, check_consistent_length
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from .utils.validation import _check_sample_weight
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from .pipeline import Pipeline
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from .isotonic import IsotonicRegression
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from .svm import LinearSVC
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from .model_selection import check_cv, cross_val_predict
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from .utils.validation import _deprecate_positional_args
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class CalibratedClassifierCV(ClassifierMixin,
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MetaEstimatorMixin,
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BaseEstimator):
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"""Probability calibration with isotonic regression or logistic regression.
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This class uses cross-validation to both estimate the parameters of a
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classifier and subsequently calibrate a classifier. With default
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`ensemble=True`, for each cv split it
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fits a copy of the base estimator to the training subset, and calibrates it
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using the testing subset. For prediction, predicted probabilities are
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averaged across these individual calibrated classifiers. When
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`ensemble=False`, cross-validation is used to obtain unbiased predictions,
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via :func:`~sklearn.model_selection.cross_val_predict`, which are then
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used for calibration. For prediction, the base estimator, trained using all
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the data, is used. This is the method implemented when `probabilities=True`
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for :mod:`sklearn.svm` estimators.
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Already fitted classifiers can be calibrated via the parameter
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`cv="prefit"`. In this case, no cross-validation is used and all provided
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data is used for calibration. The user has to take care manually that data
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for model fitting and calibration are disjoint.
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The calibration is based on the :term:`decision_function` method of the
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`base_estimator` if it exists, else on :term:`predict_proba`.
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Read more in the :ref:`User Guide <calibration>`.
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Parameters
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----------
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base_estimator : estimator instance, default=None
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The classifier whose output need to be calibrated to provide more
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accurate `predict_proba` outputs. The default classifier is
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a :class:`~sklearn.svm.LinearSVC`.
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method : {'sigmoid', 'isotonic'}, default='sigmoid'
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The method to use for calibration. Can be 'sigmoid' which
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corresponds to Platt's method (i.e. a logistic regression model) or
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'isotonic' which is a non-parametric approach. It is not advised to
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use isotonic calibration with too few calibration samples
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``(<<1000)`` since it tends to overfit.
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cv : int, cross-validation generator, iterable or "prefit", \
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default=None
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Determines the cross-validation splitting strategy.
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Possible inputs for cv are:
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- None, to use the default 5-fold cross-validation,
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- integer, to specify the number of folds.
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- :term:`CV splitter`,
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- An iterable yielding (train, test) splits as arrays of indices.
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For integer/None inputs, if ``y`` is binary or multiclass,
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:class:`~sklearn.model_selection.StratifiedKFold` is used. If ``y`` is
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neither binary nor multiclass, :class:`~sklearn.model_selection.KFold`
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is used.
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Refer to the :ref:`User Guide <cross_validation>` for the various
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cross-validation strategies that can be used here.
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If "prefit" is passed, it is assumed that `base_estimator` has been
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fitted already and all data is used for calibration.
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.. versionchanged:: 0.22
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``cv`` default value if None changed from 3-fold to 5-fold.
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n_jobs : int, default=None
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Number of jobs to run in parallel.
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``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
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``-1`` means using all processors.
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Base estimator clones are fitted in parallel across cross-validation
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iterations. Therefore parallelism happens only when `cv != "prefit"`.
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See :term:`Glossary <n_jobs>` for more details.
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.. versionadded:: 0.24
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ensemble : bool, default=True
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Determines how the calibrator is fitted when `cv` is not `'prefit'`.
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Ignored if `cv='prefit'`.
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If `True`, the `base_estimator` is fitted using training data and
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calibrated using testing data, for each `cv` fold. The final estimator
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is an ensemble of `n_cv` fitted classifer and calibrator pairs, where
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`n_cv` is the number of cross-validation folds. The output is the
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average predicted probabilities of all pairs.
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If `False`, `cv` is used to compute unbiased predictions, via
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:func:`~sklearn.model_selection.cross_val_predict`, which are then
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used for calibration. At prediction time, the classifier used is the
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`base_estimator` trained on all the data.
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Note that this method is also internally implemented in
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:mod:`sklearn.svm` estimators with the `probabilities=True` parameter.
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.. versionadded:: 0.24
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Attributes
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----------
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classes_ : ndarray of shape (n_classes,)
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The class labels.
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calibrated_classifiers_ : list (len() equal to cv or 1 if `cv="prefit"` \
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or `ensemble=False`)
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The list of classifier and calibrator pairs.
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- When `cv="prefit"`, the fitted `base_estimator` and fitted
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calibrator.
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- When `cv` is not "prefit" and `ensemble=True`, `n_cv` fitted
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`base_estimator` and calibrator pairs. `n_cv` is the number of
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cross-validation folds.
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- When `cv` is not "prefit" and `ensemble=False`, the `base_estimator`,
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fitted on all the data, and fitted calibrator.
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.. versionchanged:: 0.24
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Single calibrated classifier case when `ensemble=False`.
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Examples
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--------
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>>> from sklearn.datasets import make_classification
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>>> from sklearn.naive_bayes import GaussianNB
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>>> from sklearn.calibration import CalibratedClassifierCV
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>>> X, y = make_classification(n_samples=100, n_features=2,
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... n_redundant=0, random_state=42)
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>>> base_clf = GaussianNB()
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>>> calibrated_clf = CalibratedClassifierCV(base_estimator=base_clf, cv=3)
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>>> calibrated_clf.fit(X, y)
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CalibratedClassifierCV(base_estimator=GaussianNB(), cv=3)
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>>> len(calibrated_clf.calibrated_classifiers_)
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3
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>>> calibrated_clf.predict_proba(X)[:5, :]
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array([[0.110..., 0.889...],
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[0.072..., 0.927...],
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[0.928..., 0.071...],
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[0.928..., 0.071...],
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[0.071..., 0.928...]])
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>>> from sklearn.model_selection import train_test_split
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>>> X, y = make_classification(n_samples=100, n_features=2,
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... n_redundant=0, random_state=42)
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>>> X_train, X_calib, y_train, y_calib = train_test_split(
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... X, y, random_state=42
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... )
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>>> base_clf = GaussianNB()
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>>> base_clf.fit(X_train, y_train)
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GaussianNB()
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>>> calibrated_clf = CalibratedClassifierCV(
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... base_estimator=base_clf,
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... cv="prefit"
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... )
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>>> calibrated_clf.fit(X_calib, y_calib)
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CalibratedClassifierCV(base_estimator=GaussianNB(), cv='prefit')
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>>> len(calibrated_clf.calibrated_classifiers_)
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1
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>>> calibrated_clf.predict_proba([[-0.5, 0.5]])
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array([[0.936..., 0.063...]])
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References
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----------
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.. [1] Obtaining calibrated probability estimates from decision trees
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and naive Bayesian classifiers, B. Zadrozny & C. Elkan, ICML 2001
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.. [2] Transforming Classifier Scores into Accurate Multiclass
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Probability Estimates, B. Zadrozny & C. Elkan, (KDD 2002)
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.. [3] Probabilistic Outputs for Support Vector Machines and Comparisons to
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Regularized Likelihood Methods, J. Platt, (1999)
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.. [4] Predicting Good Probabilities with Supervised Learning,
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A. Niculescu-Mizil & R. Caruana, ICML 2005
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"""
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@_deprecate_positional_args
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def __init__(self, base_estimator=None, *, method='sigmoid',
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cv=None, n_jobs=None, ensemble=True):
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self.base_estimator = base_estimator
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self.method = method
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self.cv = cv
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self.n_jobs = n_jobs
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self.ensemble = ensemble
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def fit(self, X, y, sample_weight=None):
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"""Fit the calibrated model.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Training data.
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y : array-like of shape (n_samples,)
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Target values.
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sample_weight : array-like of shape (n_samples,), default=None
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Sample weights. If None, then samples are equally weighted.
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Returns
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-------
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self : object
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Returns an instance of self.
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"""
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check_classification_targets(y)
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X, y = indexable(X, y)
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if self.base_estimator is None:
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# we want all classifiers that don't expose a random_state
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# to be deterministic (and we don't want to expose this one).
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base_estimator = LinearSVC(random_state=0)
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else:
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base_estimator = self.base_estimator
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self.calibrated_classifiers_ = []
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if self.cv == "prefit":
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# `classes_` and `n_features_in_` should be consistent with that
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# of base_estimator
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if isinstance(self.base_estimator, Pipeline):
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check_is_fitted(self.base_estimator[-1])
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else:
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check_is_fitted(self.base_estimator)
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with suppress(AttributeError):
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self.n_features_in_ = base_estimator.n_features_in_
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self.classes_ = self.base_estimator.classes_
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pred_method = _get_prediction_method(base_estimator)
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n_classes = len(self.classes_)
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predictions = _compute_predictions(pred_method, X, n_classes)
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calibrated_classifier = _fit_calibrator(
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base_estimator, predictions, y, self.classes_, self.method,
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sample_weight
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)
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self.calibrated_classifiers_.append(calibrated_classifier)
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else:
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X, y = self._validate_data(
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X, y, accept_sparse=['csc', 'csr', 'coo'],
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force_all_finite=False, allow_nd=True
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)
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# Set `classes_` using all `y`
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label_encoder_ = LabelEncoder().fit(y)
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self.classes_ = label_encoder_.classes_
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n_classes = len(self.classes_)
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# sample_weight checks
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fit_parameters = signature(base_estimator.fit).parameters
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supports_sw = "sample_weight" in fit_parameters
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if sample_weight is not None:
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sample_weight = _check_sample_weight(sample_weight, X)
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if not supports_sw:
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estimator_name = type(base_estimator).__name__
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warnings.warn(f"Since {estimator_name} does not support "
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"sample_weights, sample weights will only be"
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" used for the calibration itself.")
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# Check that each cross-validation fold can have at least one
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# example per class
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if isinstance(self.cv, int):
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n_folds = self.cv
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elif hasattr(self.cv, "n_splits"):
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n_folds = self.cv.n_splits
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else:
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n_folds = None
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if n_folds and np.any([np.sum(y == class_) < n_folds
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for class_ in self.classes_]):
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raise ValueError(f"Requesting {n_folds}-fold "
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"cross-validation but provided less than "
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f"{n_folds} examples for at least one class.")
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cv = check_cv(self.cv, y, classifier=True)
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if self.ensemble:
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parallel = Parallel(n_jobs=self.n_jobs)
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self.calibrated_classifiers_ = parallel(
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delayed(_fit_classifier_calibrator_pair)(
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clone(base_estimator), X, y, train=train, test=test,
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method=self.method, classes=self.classes_,
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supports_sw=supports_sw, sample_weight=sample_weight)
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for train, test in cv.split(X, y)
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)
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else:
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this_estimator = clone(base_estimator)
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method_name = _get_prediction_method(this_estimator).__name__
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pred_method = partial(
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cross_val_predict, estimator=this_estimator, X=X, y=y,
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cv=cv, method=method_name, n_jobs=self.n_jobs
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)
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predictions = _compute_predictions(pred_method, X, n_classes)
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if sample_weight is not None and supports_sw:
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this_estimator.fit(X, y, sample_weight)
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else:
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this_estimator.fit(X, y)
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calibrated_classifier = _fit_calibrator(
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this_estimator, predictions, y, self.classes_, self.method,
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sample_weight
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)
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self.calibrated_classifiers_.append(calibrated_classifier)
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return self
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def predict_proba(self, X):
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"""Calibrated probabilities of classification.
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This function returns calibrated probabilities of classification
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according to each class on an array of test vectors X.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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The samples.
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Returns
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-------
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C : ndarray of shape (n_samples, n_classes)
|
||
|
|
The predicted probas.
|
||
|
|
"""
|
||
|
|
check_is_fitted(self)
|
||
|
|
X = check_array(X, accept_sparse=['csc', 'csr', 'coo'],
|
||
|
|
force_all_finite=False)
|
||
|
|
# Compute the arithmetic mean of the predictions of the calibrated
|
||
|
|
# classifiers
|
||
|
|
mean_proba = np.zeros((X.shape[0], len(self.classes_)))
|
||
|
|
for calibrated_classifier in self.calibrated_classifiers_:
|
||
|
|
proba = calibrated_classifier.predict_proba(X)
|
||
|
|
mean_proba += proba
|
||
|
|
|
||
|
|
mean_proba /= len(self.calibrated_classifiers_)
|
||
|
|
|
||
|
|
return mean_proba
|
||
|
|
|
||
|
|
def predict(self, X):
|
||
|
|
"""Predict the target of new samples. The predicted class is the
|
||
|
|
class that has the highest probability, and can thus be different
|
||
|
|
from the prediction of the uncalibrated classifier.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples, n_features)
|
||
|
|
The samples.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
C : ndarray of shape (n_samples,)
|
||
|
|
The predicted class.
|
||
|
|
"""
|
||
|
|
check_is_fitted(self)
|
||
|
|
return self.classes_[np.argmax(self.predict_proba(X), axis=1)]
|
||
|
|
|
||
|
|
def _more_tags(self):
|
||
|
|
return {
|
||
|
|
'_xfail_checks': {
|
||
|
|
'check_sample_weights_invariance':
|
||
|
|
'zero sample_weight is not equivalent to removing samples',
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
def _fit_classifier_calibrator_pair(estimator, X, y, train, test, supports_sw,
|
||
|
|
method, classes, sample_weight=None):
|
||
|
|
"""Fit a classifier/calibration pair on a given train/test split.
|
||
|
|
|
||
|
|
Fit the classifier on the train set, compute its predictions on the test
|
||
|
|
set and use the predictions as input to fit the calibrator along with the
|
||
|
|
test labels.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
estimator : estimator instance
|
||
|
|
Cloned base estimator.
|
||
|
|
|
||
|
|
X : array-like, shape (n_samples, n_features)
|
||
|
|
Sample data.
|
||
|
|
|
||
|
|
y : array-like, shape (n_samples,)
|
||
|
|
Targets.
|
||
|
|
|
||
|
|
train : ndarray, shape (n_train_indicies,)
|
||
|
|
Indices of the training subset.
|
||
|
|
|
||
|
|
test : ndarray, shape (n_test_indicies,)
|
||
|
|
Indices of the testing subset.
|
||
|
|
|
||
|
|
supports_sw : bool
|
||
|
|
Whether or not the `estimator` supports sample weights.
|
||
|
|
|
||
|
|
method : {'sigmoid', 'isotonic'}
|
||
|
|
Method to use for calibration.
|
||
|
|
|
||
|
|
classes : ndarray, shape (n_classes,)
|
||
|
|
The target classes.
|
||
|
|
|
||
|
|
sample_weight : array-like, default=None
|
||
|
|
Sample weights for `X`.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
calibrated_classifier : _CalibratedClassifier instance
|
||
|
|
"""
|
||
|
|
if sample_weight is not None and supports_sw:
|
||
|
|
estimator.fit(X[train], y[train],
|
||
|
|
sample_weight=sample_weight[train])
|
||
|
|
else:
|
||
|
|
estimator.fit(X[train], y[train])
|
||
|
|
|
||
|
|
n_classes = len(classes)
|
||
|
|
pred_method = _get_prediction_method(estimator)
|
||
|
|
predictions = _compute_predictions(pred_method, X[test], n_classes)
|
||
|
|
|
||
|
|
sw = None if sample_weight is None else sample_weight[test]
|
||
|
|
calibrated_classifier = _fit_calibrator(
|
||
|
|
estimator, predictions, y[test], classes, method, sample_weight=sw
|
||
|
|
)
|
||
|
|
return calibrated_classifier
|
||
|
|
|
||
|
|
|
||
|
|
def _get_prediction_method(clf):
|
||
|
|
"""Return prediction method.
|
||
|
|
|
||
|
|
`decision_function` method of `clf` returned, if it
|
||
|
|
exists, otherwise `predict_proba` method returned.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
clf : Estimator instance
|
||
|
|
Fitted classifier to obtain the prediction method from.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
prediction_method : callable
|
||
|
|
The prediction method.
|
||
|
|
"""
|
||
|
|
if hasattr(clf, 'decision_function'):
|
||
|
|
method = getattr(clf, 'decision_function')
|
||
|
|
elif hasattr(clf, 'predict_proba'):
|
||
|
|
method = getattr(clf, 'predict_proba')
|
||
|
|
else:
|
||
|
|
raise RuntimeError("'base_estimator' has no 'decision_function' or "
|
||
|
|
"'predict_proba' method.")
|
||
|
|
return method
|
||
|
|
|
||
|
|
|
||
|
|
def _compute_predictions(pred_method, X, n_classes):
|
||
|
|
"""Return predictions for `X` and reshape binary outputs to shape
|
||
|
|
(n_samples, 1).
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
pred_method : callable
|
||
|
|
Prediction method.
|
||
|
|
|
||
|
|
X : array-like or None
|
||
|
|
Data used to obtain predictions.
|
||
|
|
|
||
|
|
n_classes : int
|
||
|
|
Number of classes present.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
predictions : array-like, shape (X.shape[0], len(clf.classes_))
|
||
|
|
The predictions. Note if there are 2 classes, array is of shape
|
||
|
|
(X.shape[0], 1).
|
||
|
|
"""
|
||
|
|
predictions = pred_method(X=X)
|
||
|
|
if hasattr(pred_method, '__name__'):
|
||
|
|
method_name = pred_method.__name__
|
||
|
|
else:
|
||
|
|
method_name = signature(pred_method).parameters['method'].default
|
||
|
|
|
||
|
|
if method_name == 'decision_function':
|
||
|
|
if predictions.ndim == 1:
|
||
|
|
predictions = predictions[:, np.newaxis]
|
||
|
|
elif method_name == 'predict_proba':
|
||
|
|
if n_classes == 2:
|
||
|
|
predictions = predictions[:, 1:]
|
||
|
|
else: # pragma: no cover
|
||
|
|
# this branch should be unreachable.
|
||
|
|
raise ValueError(f"Invalid prediction method: {method_name}")
|
||
|
|
return predictions
|
||
|
|
|
||
|
|
|
||
|
|
def _fit_calibrator(clf, predictions, y, classes, method, sample_weight=None):
|
||
|
|
"""Fit calibrator(s) and return a `_CalibratedClassifier`
|
||
|
|
instance.
|
||
|
|
|
||
|
|
`n_classes` (i.e. `len(clf.classes_)`) calibrators are fitted.
|
||
|
|
However, if `n_classes` equals 2, one calibrator is fitted.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
clf : estimator instance
|
||
|
|
Fitted classifier.
|
||
|
|
|
||
|
|
predictions : array-like, shape (n_samples, n_classes) or (n_samples, 1) \
|
||
|
|
when binary.
|
||
|
|
Raw predictions returned by the un-calibrated base classifier.
|
||
|
|
|
||
|
|
y : array-like, shape (n_samples,)
|
||
|
|
The targets.
|
||
|
|
|
||
|
|
classes : ndarray, shape (n_classes,)
|
||
|
|
All the prediction classes.
|
||
|
|
|
||
|
|
method : {'sigmoid', 'isotonic'}
|
||
|
|
The method to use for calibration.
|
||
|
|
|
||
|
|
sample_weight : ndarray, shape (n_samples,), default=None
|
||
|
|
Sample weights. If None, then samples are equally weighted.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
pipeline : _CalibratedClassifier instance
|
||
|
|
"""
|
||
|
|
Y = label_binarize(y, classes=classes)
|
||
|
|
label_encoder = LabelEncoder().fit(classes)
|
||
|
|
pos_class_indices = label_encoder.transform(clf.classes_)
|
||
|
|
calibrators = []
|
||
|
|
for class_idx, this_pred in zip(pos_class_indices, predictions.T):
|
||
|
|
if method == 'isotonic':
|
||
|
|
calibrator = IsotonicRegression(out_of_bounds='clip')
|
||
|
|
elif method == 'sigmoid':
|
||
|
|
calibrator = _SigmoidCalibration()
|
||
|
|
else:
|
||
|
|
raise ValueError("'method' should be one of: 'sigmoid' or "
|
||
|
|
f"'isotonic'. Got {method}.")
|
||
|
|
calibrator.fit(this_pred, Y[:, class_idx], sample_weight)
|
||
|
|
calibrators.append(calibrator)
|
||
|
|
|
||
|
|
pipeline = _CalibratedClassifier(
|
||
|
|
clf, calibrators, method=method, classes=classes
|
||
|
|
)
|
||
|
|
return pipeline
|
||
|
|
|
||
|
|
|
||
|
|
class _CalibratedClassifier:
|
||
|
|
"""Pipeline-like chaining a fitted classifier and its fitted calibrators.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
base_estimator : estimator instance
|
||
|
|
Fitted classifier.
|
||
|
|
|
||
|
|
calibrators : list of fitted estimator instances
|
||
|
|
List of fitted calibrators (either 'IsotonicRegression' or
|
||
|
|
'_SigmoidCalibration'). The number of calibrators equals the number of
|
||
|
|
classes. However, if there are 2 classes, the list contains only one
|
||
|
|
fitted calibrator.
|
||
|
|
|
||
|
|
classes : array-like of shape (n_classes,)
|
||
|
|
All the prediction classes.
|
||
|
|
|
||
|
|
method : {'sigmoid', 'isotonic'}, default='sigmoid'
|
||
|
|
The method to use for calibration. Can be 'sigmoid' which
|
||
|
|
corresponds to Platt's method or 'isotonic' which is a
|
||
|
|
non-parametric approach based on isotonic regression.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
calibrators_ : list of fitted estimator instances
|
||
|
|
Same as `calibrators`. Exposed for backward-compatibility. Use
|
||
|
|
`calibrators` instead.
|
||
|
|
|
||
|
|
.. deprecated:: 0.24
|
||
|
|
`calibrators_` is deprecated from 0.24 and will be removed in
|
||
|
|
1.1 (renaming of 0.26). Use `calibrators` instead.
|
||
|
|
"""
|
||
|
|
def __init__(self, base_estimator, calibrators, *, classes,
|
||
|
|
method='sigmoid'):
|
||
|
|
self.base_estimator = base_estimator
|
||
|
|
self.calibrators = calibrators
|
||
|
|
self.classes = classes
|
||
|
|
self.method = method
|
||
|
|
|
||
|
|
# TODO: Remove in 1.1
|
||
|
|
# mypy error: Decorated property not supported
|
||
|
|
@deprecated( # type: ignore
|
||
|
|
"calibrators_ is deprecated in 0.24 and will be removed in 1.1"
|
||
|
|
"(renaming of 0.26). Use calibrators instead."
|
||
|
|
)
|
||
|
|
@property
|
||
|
|
def calibrators_(self):
|
||
|
|
return self.calibrators
|
||
|
|
|
||
|
|
def predict_proba(self, X):
|
||
|
|
"""Calculate calibrated probabilities.
|
||
|
|
|
||
|
|
Calculates classification calibrated probabilities
|
||
|
|
for each class, in a one-vs-all manner, for `X`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : ndarray of shape (n_samples, n_features)
|
||
|
|
The sample data.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
proba : array, shape (n_samples, n_classes)
|
||
|
|
The predicted probabilities. Can be exact zeros.
|
||
|
|
"""
|
||
|
|
n_classes = len(self.classes)
|
||
|
|
pred_method = _get_prediction_method(self.base_estimator)
|
||
|
|
predictions = _compute_predictions(pred_method, X, n_classes)
|
||
|
|
|
||
|
|
label_encoder = LabelEncoder().fit(self.classes)
|
||
|
|
pos_class_indices = label_encoder.transform(
|
||
|
|
self.base_estimator.classes_
|
||
|
|
)
|
||
|
|
|
||
|
|
proba = np.zeros((X.shape[0], n_classes))
|
||
|
|
for class_idx, this_pred, calibrator in \
|
||
|
|
zip(pos_class_indices, predictions.T, self.calibrators):
|
||
|
|
if n_classes == 2:
|
||
|
|
# When binary, `predictions` consists only of predictions for
|
||
|
|
# clf.classes_[1] but `pos_class_indices` = 0
|
||
|
|
class_idx += 1
|
||
|
|
proba[:, class_idx] = calibrator.predict(this_pred)
|
||
|
|
|
||
|
|
# Normalize the probabilities
|
||
|
|
if n_classes == 2:
|
||
|
|
proba[:, 0] = 1. - proba[:, 1]
|
||
|
|
else:
|
||
|
|
proba /= np.sum(proba, axis=1)[:, np.newaxis]
|
||
|
|
|
||
|
|
# XXX : for some reason all probas can be 0
|
||
|
|
proba[np.isnan(proba)] = 1. / n_classes
|
||
|
|
|
||
|
|
# Deal with cases where the predicted probability minimally exceeds 1.0
|
||
|
|
proba[(1.0 < proba) & (proba <= 1.0 + 1e-5)] = 1.0
|
||
|
|
|
||
|
|
return proba
|
||
|
|
|
||
|
|
|
||
|
|
def _sigmoid_calibration(predictions, y, sample_weight=None):
|
||
|
|
"""Probability Calibration with sigmoid method (Platt 2000)
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
predictions : ndarray of shape (n_samples,)
|
||
|
|
The decision function or predict proba for the samples.
|
||
|
|
|
||
|
|
y : ndarray of shape (n_samples,)
|
||
|
|
The targets.
|
||
|
|
|
||
|
|
sample_weight : array-like of shape (n_samples,), default=None
|
||
|
|
Sample weights. If None, then samples are equally weighted.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
a : float
|
||
|
|
The slope.
|
||
|
|
|
||
|
|
b : float
|
||
|
|
The intercept.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
Platt, "Probabilistic Outputs for Support Vector Machines"
|
||
|
|
"""
|
||
|
|
predictions = column_or_1d(predictions)
|
||
|
|
y = column_or_1d(y)
|
||
|
|
|
||
|
|
F = predictions # F follows Platt's notations
|
||
|
|
|
||
|
|
# Bayesian priors (see Platt end of section 2.2)
|
||
|
|
prior0 = float(np.sum(y <= 0))
|
||
|
|
prior1 = y.shape[0] - prior0
|
||
|
|
T = np.zeros(y.shape)
|
||
|
|
T[y > 0] = (prior1 + 1.) / (prior1 + 2.)
|
||
|
|
T[y <= 0] = 1. / (prior0 + 2.)
|
||
|
|
T1 = 1. - T
|
||
|
|
|
||
|
|
def objective(AB):
|
||
|
|
# From Platt (beginning of Section 2.2)
|
||
|
|
P = expit(-(AB[0] * F + AB[1]))
|
||
|
|
loss = -(xlogy(T, P) + xlogy(T1, 1. - P))
|
||
|
|
if sample_weight is not None:
|
||
|
|
return (sample_weight * loss).sum()
|
||
|
|
else:
|
||
|
|
return loss.sum()
|
||
|
|
|
||
|
|
def grad(AB):
|
||
|
|
# gradient of the objective function
|
||
|
|
P = expit(-(AB[0] * F + AB[1]))
|
||
|
|
TEP_minus_T1P = T - P
|
||
|
|
if sample_weight is not None:
|
||
|
|
TEP_minus_T1P *= sample_weight
|
||
|
|
dA = np.dot(TEP_minus_T1P, F)
|
||
|
|
dB = np.sum(TEP_minus_T1P)
|
||
|
|
return np.array([dA, dB])
|
||
|
|
|
||
|
|
AB0 = np.array([0., log((prior0 + 1.) / (prior1 + 1.))])
|
||
|
|
AB_ = fmin_bfgs(objective, AB0, fprime=grad, disp=False)
|
||
|
|
return AB_[0], AB_[1]
|
||
|
|
|
||
|
|
|
||
|
|
class _SigmoidCalibration(RegressorMixin, BaseEstimator):
|
||
|
|
"""Sigmoid regression model.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
a_ : float
|
||
|
|
The slope.
|
||
|
|
|
||
|
|
b_ : float
|
||
|
|
The intercept.
|
||
|
|
"""
|
||
|
|
def fit(self, X, y, sample_weight=None):
|
||
|
|
"""Fit the model using X, y as training data.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
X : array-like of shape (n_samples,)
|
||
|
|
Training data.
|
||
|
|
|
||
|
|
y : array-like of shape (n_samples,)
|
||
|
|
Training target.
|
||
|
|
|
||
|
|
sample_weight : array-like of shape (n_samples,), default=None
|
||
|
|
Sample weights. If None, then samples are equally weighted.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
self : object
|
||
|
|
Returns an instance of self.
|
||
|
|
"""
|
||
|
|
X = column_or_1d(X)
|
||
|
|
y = column_or_1d(y)
|
||
|
|
X, y = indexable(X, y)
|
||
|
|
|
||
|
|
self.a_, self.b_ = _sigmoid_calibration(X, y, sample_weight)
|
||
|
|
return self
|
||
|
|
|
||
|
|
def predict(self, T):
|
||
|
|
"""Predict new data by linear interpolation.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
T : array-like of shape (n_samples,)
|
||
|
|
Data to predict from.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
T_ : ndarray of shape (n_samples,)
|
||
|
|
The predicted data.
|
||
|
|
"""
|
||
|
|
T = column_or_1d(T)
|
||
|
|
return expit(-(self.a_ * T + self.b_))
|
||
|
|
|
||
|
|
|
||
|
|
@_deprecate_positional_args
|
||
|
|
def calibration_curve(y_true, y_prob, *, normalize=False, n_bins=5,
|
||
|
|
strategy='uniform'):
|
||
|
|
"""Compute true and predicted probabilities for a calibration curve.
|
||
|
|
|
||
|
|
The method assumes the inputs come from a binary classifier, and
|
||
|
|
discretize the [0, 1] interval into bins.
|
||
|
|
|
||
|
|
Calibration curves may also be referred to as reliability diagrams.
|
||
|
|
|
||
|
|
Read more in the :ref:`User Guide <calibration>`.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
y_true : array-like of shape (n_samples,)
|
||
|
|
True targets.
|
||
|
|
|
||
|
|
y_prob : array-like of shape (n_samples,)
|
||
|
|
Probabilities of the positive class.
|
||
|
|
|
||
|
|
normalize : bool, default=False
|
||
|
|
Whether y_prob needs to be normalized into the [0, 1] interval, i.e.
|
||
|
|
is not a proper probability. If True, the smallest value in y_prob
|
||
|
|
is linearly mapped onto 0 and the largest one onto 1.
|
||
|
|
|
||
|
|
n_bins : int, default=5
|
||
|
|
Number of bins to discretize the [0, 1] interval. A bigger number
|
||
|
|
requires more data. Bins with no samples (i.e. without
|
||
|
|
corresponding values in `y_prob`) will not be returned, thus the
|
||
|
|
returned arrays may have less than `n_bins` values.
|
||
|
|
|
||
|
|
strategy : {'uniform', 'quantile'}, default='uniform'
|
||
|
|
Strategy used to define the widths of the bins.
|
||
|
|
|
||
|
|
uniform
|
||
|
|
The bins have identical widths.
|
||
|
|
quantile
|
||
|
|
The bins have the same number of samples and depend on `y_prob`.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
prob_true : ndarray of shape (n_bins,) or smaller
|
||
|
|
The proportion of samples whose class is the positive class, in each
|
||
|
|
bin (fraction of positives).
|
||
|
|
|
||
|
|
prob_pred : ndarray of shape (n_bins,) or smaller
|
||
|
|
The mean predicted probability in each bin.
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
Alexandru Niculescu-Mizil and Rich Caruana (2005) Predicting Good
|
||
|
|
Probabilities With Supervised Learning, in Proceedings of the 22nd
|
||
|
|
International Conference on Machine Learning (ICML).
|
||
|
|
See section 4 (Qualitative Analysis of Predictions).
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> from sklearn.calibration import calibration_curve
|
||
|
|
>>> y_true = np.array([0, 0, 0, 0, 1, 1, 1, 1, 1])
|
||
|
|
>>> y_pred = np.array([0.1, 0.2, 0.3, 0.4, 0.65, 0.7, 0.8, 0.9, 1.])
|
||
|
|
>>> prob_true, prob_pred = calibration_curve(y_true, y_pred, n_bins=3)
|
||
|
|
>>> prob_true
|
||
|
|
array([0. , 0.5, 1. ])
|
||
|
|
>>> prob_pred
|
||
|
|
array([0.2 , 0.525, 0.85 ])
|
||
|
|
"""
|
||
|
|
y_true = column_or_1d(y_true)
|
||
|
|
y_prob = column_or_1d(y_prob)
|
||
|
|
check_consistent_length(y_true, y_prob)
|
||
|
|
|
||
|
|
if normalize: # Normalize predicted values into interval [0, 1]
|
||
|
|
y_prob = (y_prob - y_prob.min()) / (y_prob.max() - y_prob.min())
|
||
|
|
elif y_prob.min() < 0 or y_prob.max() > 1:
|
||
|
|
raise ValueError("y_prob has values outside [0, 1] and normalize is "
|
||
|
|
"set to False.")
|
||
|
|
|
||
|
|
labels = np.unique(y_true)
|
||
|
|
if len(labels) > 2:
|
||
|
|
raise ValueError("Only binary classification is supported. "
|
||
|
|
"Provided labels %s." % labels)
|
||
|
|
y_true = label_binarize(y_true, classes=labels)[:, 0]
|
||
|
|
|
||
|
|
if strategy == 'quantile': # Determine bin edges by distribution of data
|
||
|
|
quantiles = np.linspace(0, 1, n_bins + 1)
|
||
|
|
bins = np.percentile(y_prob, quantiles * 100)
|
||
|
|
bins[-1] = bins[-1] + 1e-8
|
||
|
|
elif strategy == 'uniform':
|
||
|
|
bins = np.linspace(0., 1. + 1e-8, n_bins + 1)
|
||
|
|
else:
|
||
|
|
raise ValueError("Invalid entry to 'strategy' input. Strategy "
|
||
|
|
"must be either 'quantile' or 'uniform'.")
|
||
|
|
|
||
|
|
binids = np.digitize(y_prob, bins) - 1
|
||
|
|
|
||
|
|
bin_sums = np.bincount(binids, weights=y_prob, minlength=len(bins))
|
||
|
|
bin_true = np.bincount(binids, weights=y_true, minlength=len(bins))
|
||
|
|
bin_total = np.bincount(binids, minlength=len(bins))
|
||
|
|
|
||
|
|
nonzero = bin_total != 0
|
||
|
|
prob_true = bin_true[nonzero] / bin_total[nonzero]
|
||
|
|
prob_pred = bin_sums[nonzero] / bin_total[nonzero]
|
||
|
|
|
||
|
|
return prob_true, prob_pred
|