1409 lines
48 KiB
Python
1409 lines
48 KiB
Python
"""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 math import log
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from numbers import Integral, Real
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import numpy as np
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from scipy.optimize import minimize
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from scipy.special import expit
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from sklearn.utils import Bunch
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from ._loss import HalfBinomialLoss
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from .base import (
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BaseEstimator,
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ClassifierMixin,
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MetaEstimatorMixin,
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RegressorMixin,
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_fit_context,
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clone,
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)
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from .isotonic import IsotonicRegression
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from .model_selection import check_cv, cross_val_predict
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from .preprocessing import LabelEncoder, label_binarize
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from .svm import LinearSVC
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from .utils import (
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_safe_indexing,
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column_or_1d,
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indexable,
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)
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from .utils._param_validation import (
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HasMethods,
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Interval,
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StrOptions,
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validate_params,
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)
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from .utils._plotting import _BinaryClassifierCurveDisplayMixin
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from .utils._response import _get_response_values, _process_predict_proba
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from .utils.metadata_routing import (
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MetadataRouter,
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MethodMapping,
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_routing_enabled,
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process_routing,
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)
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from .utils.multiclass import check_classification_targets
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from .utils.parallel import Parallel, delayed
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from .utils.validation import (
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_check_method_params,
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_check_pos_label_consistency,
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_check_response_method,
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_check_sample_weight,
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_num_samples,
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check_consistent_length,
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check_is_fitted,
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)
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class CalibratedClassifierCV(ClassifierMixin, MetaEstimatorMixin, 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 prediction method implemented when
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`probabilities=True` for :class:`~sklearn.svm.SVC` and :class:`~sklearn.svm.NuSVC`
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estimators (see :ref:`User Guide <scores_probabilities>` for details).
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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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`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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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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.. versionadded:: 1.2
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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 `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 `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 classifier 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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`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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n_features_in_ : int
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Number of features seen during :term:`fit`. Only defined if the
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underlying estimator exposes such an attribute when fit.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Only defined if the
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underlying estimator exposes such an attribute when fit.
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.. versionadded:: 1.0
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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 `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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`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 `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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See Also
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--------
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calibration_curve : Compute true and predicted probabilities
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for a calibration curve.
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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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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_clf, cv=3)
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>>> calibrated_clf.fit(X, y)
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CalibratedClassifierCV(...)
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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(base_clf, cv="prefit")
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>>> calibrated_clf.fit(X_calib, y_calib)
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CalibratedClassifierCV(...)
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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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"""
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_parameter_constraints: dict = {
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"estimator": [
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HasMethods(["fit", "predict_proba"]),
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HasMethods(["fit", "decision_function"]),
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None,
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],
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"method": [StrOptions({"isotonic", "sigmoid"})],
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"cv": ["cv_object", StrOptions({"prefit"})],
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"n_jobs": [Integral, None],
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"ensemble": ["boolean"],
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}
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def __init__(
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self,
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estimator=None,
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*,
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method="sigmoid",
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cv=None,
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n_jobs=None,
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ensemble=True,
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):
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self.estimator = 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 _get_estimator(self):
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"""Resolve which estimator to return (default is LinearSVC)"""
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if self.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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estimator = LinearSVC(random_state=0)
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if _routing_enabled():
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estimator.set_fit_request(sample_weight=True)
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else:
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estimator = self.estimator
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return estimator
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@_fit_context(
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# CalibratedClassifierCV.estimator is not validated yet
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prefer_skip_nested_validation=False
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)
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def fit(self, X, y, sample_weight=None, **fit_params):
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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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**fit_params : dict
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Parameters to pass to the `fit` method of the underlying
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classifier.
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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 sample_weight is not None:
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sample_weight = _check_sample_weight(sample_weight, X)
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estimator = self._get_estimator()
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self.calibrated_classifiers_ = []
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if self.cv == "prefit":
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# `classes_` should be consistent with that of estimator
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check_is_fitted(self.estimator, attributes=["classes_"])
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self.classes_ = self.estimator.classes_
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predictions, _ = _get_response_values(
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estimator,
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X,
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response_method=["decision_function", "predict_proba"],
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)
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if predictions.ndim == 1:
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# Reshape binary output from `(n_samples,)` to `(n_samples, 1)`
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predictions = predictions.reshape(-1, 1)
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calibrated_classifier = _fit_calibrator(
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estimator,
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predictions,
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y,
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self.classes_,
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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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# 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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if _routing_enabled():
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routed_params = process_routing(
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self,
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"fit",
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sample_weight=sample_weight,
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**fit_params,
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)
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else:
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# sample_weight checks
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fit_parameters = signature(estimator.fit).parameters
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supports_sw = "sample_weight" in fit_parameters
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if sample_weight is not None and not supports_sw:
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estimator_name = type(estimator).__name__
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warnings.warn(
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f"Since {estimator_name} does not appear to accept"
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" sample_weight, sample weights will only be used for the"
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" calibration itself. This can be caused by a limitation of"
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" the current scikit-learn API. See the following issue for"
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" more details:"
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" https://github.com/scikit-learn/scikit-learn/issues/21134."
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" Be warned that the result of the calibration is likely to be"
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" incorrect."
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)
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routed_params = Bunch()
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routed_params.splitter = Bunch(split={}) # no routing for splitter
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routed_params.estimator = Bunch(fit=fit_params)
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if sample_weight is not None and supports_sw:
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routed_params.estimator.fit["sample_weight"] = sample_weight
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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.unique(y, return_counts=True)[1] < n_folds):
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raise ValueError(
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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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)
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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(estimator),
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X,
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y,
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train=train,
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test=test,
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method=self.method,
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classes=self.classes_,
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sample_weight=sample_weight,
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fit_params=routed_params.estimator.fit,
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)
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for train, test in cv.split(X, y, **routed_params.splitter.split)
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)
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else:
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this_estimator = clone(estimator)
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method_name = _check_response_method(
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this_estimator,
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["decision_function", "predict_proba"],
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).__name__
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predictions = cross_val_predict(
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estimator=this_estimator,
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X=X,
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y=y,
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cv=cv,
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method=method_name,
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n_jobs=self.n_jobs,
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params=routed_params.estimator.fit,
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)
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if len(self.classes_) == 2:
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# Ensure shape (n_samples, 1) in the binary case
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if method_name == "predict_proba":
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# Select the probability column of the postive class
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predictions = _process_predict_proba(
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y_pred=predictions,
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target_type="binary",
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classes=self.classes_,
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pos_label=self.classes_[1],
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)
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predictions = predictions.reshape(-1, 1)
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this_estimator.fit(X, y, **routed_params.estimator.fit)
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# Note: Here we don't pass on fit_params because the supported
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# calibrators don't support fit_params anyway
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calibrated_classifier = _fit_calibrator(
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this_estimator,
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predictions,
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y,
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self.classes_,
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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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first_clf = self.calibrated_classifiers_[0].estimator
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if hasattr(first_clf, "n_features_in_"):
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self.n_features_in_ = first_clf.n_features_in_
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if hasattr(first_clf, "feature_names_in_"):
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self.feature_names_in_ = first_clf.feature_names_in_
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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, as accepted by `estimator.predict_proba`.
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Returns
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-------
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C : ndarray of shape (n_samples, n_classes)
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The predicted probas.
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"""
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check_is_fitted(self)
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# Compute the arithmetic mean of the predictions of the calibrated
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# classifiers
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mean_proba = np.zeros((_num_samples(X), len(self.classes_)))
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for calibrated_classifier in self.calibrated_classifiers_:
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proba = calibrated_classifier.predict_proba(X)
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mean_proba += proba
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mean_proba /= len(self.calibrated_classifiers_)
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return mean_proba
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def predict(self, X):
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"""Predict the target of new samples.
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The predicted class is the class that has the highest probability,
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and can thus be different from the prediction of the uncalibrated classifier.
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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, as accepted by `estimator.predict`.
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Returns
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-------
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C : ndarray of shape (n_samples,)
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The predicted class.
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"""
|
|
check_is_fitted(self)
|
|
return self.classes_[np.argmax(self.predict_proba(X), axis=1)]
|
|
|
|
def get_metadata_routing(self):
|
|
"""Get metadata routing of this object.
|
|
|
|
Please check :ref:`User Guide <metadata_routing>` on how the routing
|
|
mechanism works.
|
|
|
|
Returns
|
|
-------
|
|
routing : MetadataRouter
|
|
A :class:`~sklearn.utils.metadata_routing.MetadataRouter` encapsulating
|
|
routing information.
|
|
"""
|
|
router = (
|
|
MetadataRouter(owner=self.__class__.__name__)
|
|
.add_self_request(self)
|
|
.add(
|
|
estimator=self._get_estimator(),
|
|
method_mapping=MethodMapping().add(caller="fit", callee="fit"),
|
|
)
|
|
.add(
|
|
splitter=self.cv,
|
|
method_mapping=MethodMapping().add(caller="fit", callee="split"),
|
|
)
|
|
)
|
|
return router
|
|
|
|
def _more_tags(self):
|
|
return {
|
|
"_xfail_checks": {
|
|
"check_sample_weights_invariance": (
|
|
"Due to the cross-validation and sample ordering, removing a sample"
|
|
" is not strictly equal to putting is weight to zero. Specific unit"
|
|
" tests are added for CalibratedClassifierCV specifically."
|
|
),
|
|
}
|
|
}
|
|
|
|
|
|
def _fit_classifier_calibrator_pair(
|
|
estimator,
|
|
X,
|
|
y,
|
|
train,
|
|
test,
|
|
method,
|
|
classes,
|
|
sample_weight=None,
|
|
fit_params=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_indices,)
|
|
Indices of the training subset.
|
|
|
|
test : ndarray, shape (n_test_indices,)
|
|
Indices of the testing subset.
|
|
|
|
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`.
|
|
|
|
fit_params : dict, default=None
|
|
Parameters to pass to the `fit` method of the underlying
|
|
classifier.
|
|
|
|
Returns
|
|
-------
|
|
calibrated_classifier : _CalibratedClassifier instance
|
|
"""
|
|
fit_params_train = _check_method_params(X, params=fit_params, indices=train)
|
|
X_train, y_train = _safe_indexing(X, train), _safe_indexing(y, train)
|
|
X_test, y_test = _safe_indexing(X, test), _safe_indexing(y, test)
|
|
|
|
estimator.fit(X_train, y_train, **fit_params_train)
|
|
|
|
predictions, _ = _get_response_values(
|
|
estimator,
|
|
X_test,
|
|
response_method=["decision_function", "predict_proba"],
|
|
)
|
|
if predictions.ndim == 1:
|
|
# Reshape binary output from `(n_samples,)` to `(n_samples, 1)`
|
|
predictions = predictions.reshape(-1, 1)
|
|
|
|
sw_test = None if sample_weight is None else _safe_indexing(sample_weight, test)
|
|
calibrated_classifier = _fit_calibrator(
|
|
estimator, predictions, y_test, classes, method, sample_weight=sw_test
|
|
)
|
|
return calibrated_classifier
|
|
|
|
|
|
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")
|
|
else: # "sigmoid"
|
|
calibrator = _SigmoidCalibration()
|
|
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
|
|
----------
|
|
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.
|
|
"""
|
|
|
|
def __init__(self, estimator, calibrators, *, classes, method="sigmoid"):
|
|
self.estimator = estimator
|
|
self.calibrators = calibrators
|
|
self.classes = classes
|
|
self.method = method
|
|
|
|
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.
|
|
"""
|
|
predictions, _ = _get_response_values(
|
|
self.estimator,
|
|
X,
|
|
response_method=["decision_function", "predict_proba"],
|
|
)
|
|
if predictions.ndim == 1:
|
|
# Reshape binary output from `(n_samples,)` to `(n_samples, 1)`
|
|
predictions = predictions.reshape(-1, 1)
|
|
|
|
n_classes = len(self.classes)
|
|
|
|
label_encoder = LabelEncoder().fit(self.classes)
|
|
pos_class_indices = label_encoder.transform(self.estimator.classes_)
|
|
|
|
proba = np.zeros((_num_samples(X), 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] = 1.0 - proba[:, 1]
|
|
else:
|
|
denominator = np.sum(proba, axis=1)[:, np.newaxis]
|
|
# In the edge case where for each class calibrator returns a null
|
|
# probability for a given sample, use the uniform distribution
|
|
# instead.
|
|
uniform_proba = np.full_like(proba, 1 / n_classes)
|
|
proba = np.divide(
|
|
proba, denominator, out=uniform_proba, where=denominator != 0
|
|
)
|
|
|
|
# Deal with cases where the predicted probability minimally exceeds 1.0
|
|
proba[(1.0 < proba) & (proba <= 1.0 + 1e-5)] = 1.0
|
|
|
|
return proba
|
|
|
|
|
|
# The max_abs_prediction_threshold was approximated using
|
|
# logit(np.finfo(np.float64).eps) which is about -36
|
|
def _sigmoid_calibration(
|
|
predictions, y, sample_weight=None, max_abs_prediction_threshold=30
|
|
):
|
|
"""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
|
|
|
|
scale_constant = 1.0
|
|
max_prediction = np.max(np.abs(F))
|
|
|
|
# If the predictions have large values we scale them in order to bring
|
|
# them within a suitable range. This has no effect on the final
|
|
# (prediction) result because linear models like Logisitic Regression
|
|
# without a penalty are invariant to multiplying the features by a
|
|
# constant.
|
|
if max_prediction >= max_abs_prediction_threshold:
|
|
scale_constant = max_prediction
|
|
# We rescale the features in a copy: inplace rescaling could confuse
|
|
# the caller and make the code harder to reason about.
|
|
F = F / scale_constant
|
|
|
|
# Bayesian priors (see Platt end of section 2.2):
|
|
# It corresponds to the number of samples, taking into account the
|
|
# `sample_weight`.
|
|
mask_negative_samples = y <= 0
|
|
if sample_weight is not None:
|
|
prior0 = (sample_weight[mask_negative_samples]).sum()
|
|
prior1 = (sample_weight[~mask_negative_samples]).sum()
|
|
else:
|
|
prior0 = float(np.sum(mask_negative_samples))
|
|
prior1 = y.shape[0] - prior0
|
|
T = np.zeros_like(y, dtype=predictions.dtype)
|
|
T[y > 0] = (prior1 + 1.0) / (prior1 + 2.0)
|
|
T[y <= 0] = 1.0 / (prior0 + 2.0)
|
|
|
|
bin_loss = HalfBinomialLoss()
|
|
|
|
def loss_grad(AB):
|
|
# .astype below is needed to ensure y_true and raw_prediction have the
|
|
# same dtype. With result = np.float64(0) * np.array([1, 2], dtype=np.float32)
|
|
# - in Numpy 2, result.dtype is float64
|
|
# - in Numpy<2, result.dtype is float32
|
|
raw_prediction = -(AB[0] * F + AB[1]).astype(dtype=predictions.dtype)
|
|
l, g = bin_loss.loss_gradient(
|
|
y_true=T,
|
|
raw_prediction=raw_prediction,
|
|
sample_weight=sample_weight,
|
|
)
|
|
loss = l.sum()
|
|
# TODO: Remove casting to np.float64 when minimum supported SciPy is 1.11.2
|
|
# With SciPy >= 1.11.2, the LBFGS implementation will cast to float64
|
|
# https://github.com/scipy/scipy/pull/18825.
|
|
# Here we cast to float64 to support SciPy < 1.11.2
|
|
grad = np.asarray([-g @ F, -g.sum()], dtype=np.float64)
|
|
return loss, grad
|
|
|
|
AB0 = np.array([0.0, log((prior0 + 1.0) / (prior1 + 1.0))])
|
|
|
|
opt_result = minimize(
|
|
loss_grad,
|
|
AB0,
|
|
method="L-BFGS-B",
|
|
jac=True,
|
|
options={
|
|
"gtol": 1e-6,
|
|
"ftol": 64 * np.finfo(float).eps,
|
|
},
|
|
)
|
|
AB_ = opt_result.x
|
|
|
|
# The tuned multiplicative parameter is converted back to the original
|
|
# input feature scale. The offset parameter does not need rescaling since
|
|
# we did not rescale the outcome variable.
|
|
return AB_[0] / scale_constant, 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_))
|
|
|
|
|
|
@validate_params(
|
|
{
|
|
"y_true": ["array-like"],
|
|
"y_prob": ["array-like"],
|
|
"pos_label": [Real, str, "boolean", None],
|
|
"n_bins": [Interval(Integral, 1, None, closed="left")],
|
|
"strategy": [StrOptions({"uniform", "quantile"})],
|
|
},
|
|
prefer_skip_nested_validation=True,
|
|
)
|
|
def calibration_curve(
|
|
y_true,
|
|
y_prob,
|
|
*,
|
|
pos_label=None,
|
|
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.
|
|
|
|
pos_label : int, float, bool or str, default=None
|
|
The label of the positive class.
|
|
|
|
.. versionadded:: 1.1
|
|
|
|
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)
|
|
pos_label = _check_pos_label_consistency(pos_label, y_true)
|
|
|
|
if y_prob.min() < 0 or y_prob.max() > 1:
|
|
raise ValueError("y_prob has values outside [0, 1].")
|
|
|
|
labels = np.unique(y_true)
|
|
if len(labels) > 2:
|
|
raise ValueError(
|
|
f"Only binary classification is supported. Provided labels {labels}."
|
|
)
|
|
y_true = y_true == pos_label
|
|
|
|
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)
|
|
elif strategy == "uniform":
|
|
bins = np.linspace(0.0, 1.0, n_bins + 1)
|
|
else:
|
|
raise ValueError(
|
|
"Invalid entry to 'strategy' input. Strategy "
|
|
"must be either 'quantile' or 'uniform'."
|
|
)
|
|
|
|
binids = np.searchsorted(bins[1:-1], y_prob)
|
|
|
|
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
|
|
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class CalibrationDisplay(_BinaryClassifierCurveDisplayMixin):
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"""Calibration curve (also known as reliability diagram) visualization.
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It is recommended to use
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:func:`~sklearn.calibration.CalibrationDisplay.from_estimator` or
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:func:`~sklearn.calibration.CalibrationDisplay.from_predictions`
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to create a `CalibrationDisplay`. All parameters are stored as attributes.
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Read more about calibration in the :ref:`User Guide <calibration>` and
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more about the scikit-learn visualization API in :ref:`visualizations`.
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.. versionadded:: 1.0
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Parameters
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----------
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prob_true : ndarray of shape (n_bins,)
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The proportion of samples whose class is the positive class (fraction
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of positives), in each bin.
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prob_pred : ndarray of shape (n_bins,)
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The mean predicted probability in each bin.
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y_prob : ndarray of shape (n_samples,)
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Probability estimates for the positive class, for each sample.
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estimator_name : str, default=None
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Name of estimator. If None, the estimator name is not shown.
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pos_label : int, float, bool or str, default=None
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The positive class when computing the calibration curve.
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By default, `pos_label` is set to `estimators.classes_[1]` when using
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`from_estimator` and set to 1 when using `from_predictions`.
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.. versionadded:: 1.1
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Attributes
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----------
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line_ : matplotlib Artist
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Calibration curve.
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ax_ : matplotlib Axes
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Axes with calibration curve.
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figure_ : matplotlib Figure
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Figure containing the curve.
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See Also
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--------
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calibration_curve : Compute true and predicted probabilities for a
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calibration curve.
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CalibrationDisplay.from_predictions : Plot calibration curve using true
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and predicted labels.
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CalibrationDisplay.from_estimator : Plot calibration curve using an
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estimator and data.
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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.model_selection import train_test_split
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>>> from sklearn.linear_model import LogisticRegression
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>>> from sklearn.calibration import calibration_curve, CalibrationDisplay
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>>> X, y = make_classification(random_state=0)
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>>> X_train, X_test, y_train, y_test = train_test_split(
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... X, y, random_state=0)
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>>> clf = LogisticRegression(random_state=0)
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>>> clf.fit(X_train, y_train)
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LogisticRegression(random_state=0)
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>>> y_prob = clf.predict_proba(X_test)[:, 1]
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>>> prob_true, prob_pred = calibration_curve(y_test, y_prob, n_bins=10)
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>>> disp = CalibrationDisplay(prob_true, prob_pred, y_prob)
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>>> disp.plot()
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<...>
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"""
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def __init__(
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self, prob_true, prob_pred, y_prob, *, estimator_name=None, pos_label=None
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):
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self.prob_true = prob_true
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self.prob_pred = prob_pred
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self.y_prob = y_prob
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self.estimator_name = estimator_name
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self.pos_label = pos_label
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def plot(self, *, ax=None, name=None, ref_line=True, **kwargs):
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"""Plot visualization.
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Extra keyword arguments will be passed to
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:func:`matplotlib.pyplot.plot`.
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Parameters
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----------
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ax : Matplotlib Axes, default=None
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Axes object to plot on. If `None`, a new figure and axes is
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created.
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name : str, default=None
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Name for labeling curve. If `None`, use `estimator_name` if
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not `None`, otherwise no labeling is shown.
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ref_line : bool, default=True
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If `True`, plots a reference line representing a perfectly
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calibrated classifier.
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**kwargs : dict
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Keyword arguments to be passed to :func:`matplotlib.pyplot.plot`.
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Returns
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-------
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display : :class:`~sklearn.calibration.CalibrationDisplay`
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Object that stores computed values.
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"""
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self.ax_, self.figure_, name = self._validate_plot_params(ax=ax, name=name)
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info_pos_label = (
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f"(Positive class: {self.pos_label})" if self.pos_label is not None else ""
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)
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line_kwargs = {"marker": "s", "linestyle": "-"}
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if name is not None:
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line_kwargs["label"] = name
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line_kwargs.update(**kwargs)
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ref_line_label = "Perfectly calibrated"
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existing_ref_line = ref_line_label in self.ax_.get_legend_handles_labels()[1]
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if ref_line and not existing_ref_line:
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self.ax_.plot([0, 1], [0, 1], "k:", label=ref_line_label)
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self.line_ = self.ax_.plot(self.prob_pred, self.prob_true, **line_kwargs)[0]
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# We always have to show the legend for at least the reference line
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self.ax_.legend(loc="lower right")
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xlabel = f"Mean predicted probability {info_pos_label}"
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ylabel = f"Fraction of positives {info_pos_label}"
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self.ax_.set(xlabel=xlabel, ylabel=ylabel)
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return self
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@classmethod
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def from_estimator(
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cls,
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estimator,
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X,
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y,
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*,
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n_bins=5,
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strategy="uniform",
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pos_label=None,
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name=None,
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ref_line=True,
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ax=None,
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**kwargs,
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):
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"""Plot calibration curve using a binary classifier and data.
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A calibration curve, also known as a reliability diagram, uses inputs
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from a binary classifier and plots the average predicted probability
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for each bin against the fraction of positive classes, on the
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y-axis.
|
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Extra keyword arguments will be passed to
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:func:`matplotlib.pyplot.plot`.
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Read more about calibration in the :ref:`User Guide <calibration>` and
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more about the scikit-learn visualization API in :ref:`visualizations`.
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.. versionadded:: 1.0
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Parameters
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----------
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estimator : estimator instance
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Fitted classifier or a fitted :class:`~sklearn.pipeline.Pipeline`
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in which the last estimator is a classifier. The classifier must
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have a :term:`predict_proba` method.
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X : {array-like, sparse matrix} of shape (n_samples, n_features)
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Input values.
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y : array-like of shape (n_samples,)
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Binary target values.
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n_bins : int, default=5
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Number of bins to discretize the [0, 1] interval into when
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calculating the calibration curve. A bigger number requires more
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data.
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strategy : {'uniform', 'quantile'}, default='uniform'
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Strategy used to define the widths of the bins.
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- `'uniform'`: The bins have identical widths.
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- `'quantile'`: The bins have the same number of samples and depend
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on predicted probabilities.
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pos_label : int, float, bool or str, default=None
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The positive class when computing the calibration curve.
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By default, `estimators.classes_[1]` is considered as the
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positive class.
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.. versionadded:: 1.1
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name : str, default=None
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Name for labeling curve. If `None`, the name of the estimator is
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used.
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ref_line : bool, default=True
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If `True`, plots a reference line representing a perfectly
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calibrated classifier.
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ax : matplotlib axes, default=None
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Axes object to plot on. If `None`, a new figure and axes is
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created.
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**kwargs : dict
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Keyword arguments to be passed to :func:`matplotlib.pyplot.plot`.
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Returns
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-------
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display : :class:`~sklearn.calibration.CalibrationDisplay`.
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Object that stores computed values.
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See Also
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--------
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CalibrationDisplay.from_predictions : Plot calibration curve using true
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and predicted labels.
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Examples
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--------
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>>> import matplotlib.pyplot as plt
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>>> from sklearn.datasets import make_classification
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>>> from sklearn.model_selection import train_test_split
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>>> from sklearn.linear_model import LogisticRegression
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>>> from sklearn.calibration import CalibrationDisplay
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>>> X, y = make_classification(random_state=0)
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>>> X_train, X_test, y_train, y_test = train_test_split(
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... X, y, random_state=0)
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>>> clf = LogisticRegression(random_state=0)
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>>> clf.fit(X_train, y_train)
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LogisticRegression(random_state=0)
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>>> disp = CalibrationDisplay.from_estimator(clf, X_test, y_test)
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>>> plt.show()
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"""
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y_prob, pos_label, name = cls._validate_and_get_response_values(
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estimator,
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X,
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y,
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response_method="predict_proba",
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pos_label=pos_label,
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name=name,
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)
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return cls.from_predictions(
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y,
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y_prob,
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n_bins=n_bins,
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strategy=strategy,
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pos_label=pos_label,
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name=name,
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ref_line=ref_line,
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ax=ax,
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**kwargs,
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)
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@classmethod
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def from_predictions(
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cls,
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y_true,
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y_prob,
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*,
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n_bins=5,
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strategy="uniform",
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pos_label=None,
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name=None,
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ref_line=True,
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ax=None,
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**kwargs,
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):
|
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"""Plot calibration curve using true labels and predicted probabilities.
|
|
|
|
Calibration curve, also known as reliability diagram, uses inputs
|
|
from a binary classifier and plots the average predicted probability
|
|
for each bin against the fraction of positive classes, on the
|
|
y-axis.
|
|
|
|
Extra keyword arguments will be passed to
|
|
:func:`matplotlib.pyplot.plot`.
|
|
|
|
Read more about calibration in the :ref:`User Guide <calibration>` and
|
|
more about the scikit-learn visualization API in :ref:`visualizations`.
|
|
|
|
.. versionadded:: 1.0
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Parameters
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----------
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y_true : array-like of shape (n_samples,)
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True labels.
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y_prob : array-like of shape (n_samples,)
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The predicted probabilities of the positive class.
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n_bins : int, default=5
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Number of bins to discretize the [0, 1] interval into when
|
|
calculating the calibration curve. A bigger number requires more
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data.
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strategy : {'uniform', 'quantile'}, default='uniform'
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Strategy used to define the widths of the bins.
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|
- `'uniform'`: The bins have identical widths.
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- `'quantile'`: The bins have the same number of samples and depend
|
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on predicted probabilities.
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pos_label : int, float, bool or str, default=None
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|
The positive class when computing the calibration curve.
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By default `pos_label` is set to 1.
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|
|
.. versionadded:: 1.1
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name : str, default=None
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Name for labeling curve.
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ref_line : bool, default=True
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|
If `True`, plots a reference line representing a perfectly
|
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calibrated classifier.
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ax : matplotlib axes, default=None
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|
Axes object to plot on. If `None`, a new figure and axes is
|
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created.
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|
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**kwargs : dict
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|
Keyword arguments to be passed to :func:`matplotlib.pyplot.plot`.
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Returns
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-------
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display : :class:`~sklearn.calibration.CalibrationDisplay`.
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|
Object that stores computed values.
|
|
|
|
See Also
|
|
--------
|
|
CalibrationDisplay.from_estimator : Plot calibration curve using an
|
|
estimator and data.
|
|
|
|
Examples
|
|
--------
|
|
>>> import matplotlib.pyplot as plt
|
|
>>> from sklearn.datasets import make_classification
|
|
>>> from sklearn.model_selection import train_test_split
|
|
>>> from sklearn.linear_model import LogisticRegression
|
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>>> from sklearn.calibration import CalibrationDisplay
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>>> X, y = make_classification(random_state=0)
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>>> X_train, X_test, y_train, y_test = train_test_split(
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... X, y, random_state=0)
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>>> clf = LogisticRegression(random_state=0)
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>>> clf.fit(X_train, y_train)
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LogisticRegression(random_state=0)
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>>> y_prob = clf.predict_proba(X_test)[:, 1]
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>>> disp = CalibrationDisplay.from_predictions(y_test, y_prob)
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>>> plt.show()
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"""
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pos_label_validated, name = cls._validate_from_predictions_params(
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y_true, y_prob, sample_weight=None, pos_label=pos_label, name=name
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)
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prob_true, prob_pred = calibration_curve(
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y_true, y_prob, n_bins=n_bins, strategy=strategy, pos_label=pos_label
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)
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disp = cls(
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prob_true=prob_true,
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prob_pred=prob_pred,
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y_prob=y_prob,
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estimator_name=name,
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pos_label=pos_label_validated,
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)
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return disp.plot(ax=ax, ref_line=ref_line, **kwargs)
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