"""Calibration of predicted probabilities.""" # Author: Alexandre Gramfort # Balazs Kegl # Jan Hendrik Metzen # Mathieu Blondel # # License: BSD 3 clause from __future__ import division import warnings from math import log import numpy as np from scipy.optimize import fmin_bfgs from sklearn.preprocessing import LabelEncoder from .base import BaseEstimator, ClassifierMixin, RegressorMixin, clone from .preprocessing import label_binarize, LabelBinarizer from .utils import check_X_y, check_array, indexable, column_or_1d from .utils.validation import check_is_fitted, check_consistent_length from .utils.fixes import signature from .isotonic import IsotonicRegression from .svm import LinearSVC from .model_selection import check_cv from .metrics.classification import _check_binary_probabilistic_predictions class CalibratedClassifierCV(BaseEstimator, ClassifierMixin): """Probability calibration with isotonic regression or sigmoid. With this class, the base_estimator is fit on the train set of the cross-validation generator and the test set is used for calibration. The probabilities for each of the folds are then averaged for prediction. In case that cv="prefit" is passed to __init__, it is assumed that base_estimator has been fitted already and all data is used for calibration. Note that data for fitting the classifier and for calibrating it must be disjoint. Read more in the :ref:`User Guide `. Parameters ---------- base_estimator : instance BaseEstimator The classifier whose output decision function needs to be calibrated to offer more accurate predict_proba outputs. If cv=prefit, the classifier must have been fit already on data. method : 'sigmoid' or 'isotonic' The method to use for calibration. Can be 'sigmoid' which corresponds to Platt's method or 'isotonic' which is a non-parametric approach. It is not advised to use isotonic calibration with too few calibration samples ``(<<1000)`` since it tends to overfit. Use sigmoids (Platt's calibration) in this case. cv : integer, cross-validation generator, iterable or "prefit", optional Determines the cross-validation splitting strategy. Possible inputs for cv are: - None, to use the default 3-fold cross-validation, - integer, to specify the number of folds. - An object to be used as a cross-validation generator. - An iterable yielding train/test splits. For integer/None inputs, if ``y`` is binary or multiclass, :class:`sklearn.model_selection.StratifiedKFold` is used. If ``y`` is neither binary nor multiclass, :class:`sklearn.model_selection.KFold` is used. Refer :ref:`User Guide ` for the various cross-validation strategies that can be used here. If "prefit" is passed, it is assumed that base_estimator has been fitted already and all data is used for calibration. Attributes ---------- classes_ : array, shape (n_classes) The class labels. calibrated_classifiers_ : list (len() equal to cv or 1 if cv == "prefit") The list of calibrated classifiers, one for each crossvalidation fold, which has been fitted on all but the validation fold and calibrated on the validation fold. References ---------- .. [1] Obtaining calibrated probability estimates from decision trees and naive Bayesian classifiers, B. Zadrozny & C. Elkan, ICML 2001 .. [2] Transforming Classifier Scores into Accurate Multiclass Probability Estimates, B. Zadrozny & C. Elkan, (KDD 2002) .. [3] Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods, J. Platt, (1999) .. [4] Predicting Good Probabilities with Supervised Learning, A. Niculescu-Mizil & R. Caruana, ICML 2005 """ def __init__(self, base_estimator=None, method='sigmoid', cv=3): self.base_estimator = base_estimator self.method = method self.cv = cv def fit(self, X, y, sample_weight=None): """Fit the calibrated model Parameters ---------- X : array-like, shape (n_samples, n_features) Training data. y : array-like, shape (n_samples,) Target values. sample_weight : array-like, shape = [n_samples] or None Sample weights. If None, then samples are equally weighted. Returns ------- self : object Returns an instance of self. """ X, y = check_X_y(X, y, accept_sparse=['csc', 'csr', 'coo'], force_all_finite=False) X, y = indexable(X, y) le = LabelBinarizer().fit(y) self.classes_ = le.classes_ # Check that each cross-validation fold can have at least one # example per class n_folds = self.cv if isinstance(self.cv, int) \ else self.cv.n_folds if hasattr(self.cv, "n_folds") else None if n_folds and \ np.any([np.sum(y == class_) < n_folds for class_ in self.classes_]): raise ValueError("Requesting %d-fold cross-validation but provided" " less than %d examples for at least one class." % (n_folds, n_folds)) self.calibrated_classifiers_ = [] if self.base_estimator is None: # we want all classifiers that don't expose a random_state # to be deterministic (and we don't want to expose this one). base_estimator = LinearSVC(random_state=0) else: base_estimator = self.base_estimator if self.cv == "prefit": calibrated_classifier = _CalibratedClassifier( base_estimator, method=self.method) if sample_weight is not None: calibrated_classifier.fit(X, y, sample_weight) else: calibrated_classifier.fit(X, y) self.calibrated_classifiers_.append(calibrated_classifier) else: cv = check_cv(self.cv, y, classifier=True) fit_parameters = signature(base_estimator.fit).parameters estimator_name = type(base_estimator).__name__ if (sample_weight is not None and "sample_weight" not in fit_parameters): warnings.warn("%s does not support sample_weight. Samples" " weights are only used for the calibration" " itself." % estimator_name) base_estimator_sample_weight = None else: if sample_weight is not None: sample_weight = check_array(sample_weight, ensure_2d=False) check_consistent_length(y, sample_weight) base_estimator_sample_weight = sample_weight for train, test in cv.split(X, y): this_estimator = clone(base_estimator) if base_estimator_sample_weight is not None: this_estimator.fit( X[train], y[train], sample_weight=base_estimator_sample_weight[train]) else: this_estimator.fit(X[train], y[train]) calibrated_classifier = _CalibratedClassifier( this_estimator, method=self.method, classes=self.classes_) if sample_weight is not None: calibrated_classifier.fit(X[test], y[test], sample_weight[test]) else: calibrated_classifier.fit(X[test], y[test]) self.calibrated_classifiers_.append(calibrated_classifier) return self def predict_proba(self, X): """Posterior probabilities of classification This function returns posterior probabilities of classification according to each class on an array of test vectors X. Parameters ---------- X : array-like, shape (n_samples, n_features) The samples. Returns ------- C : array, shape (n_samples, n_classes) The predicted probas. """ check_is_fitted(self, ["classes_", "calibrated_classifiers_"]) 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. Can be different from the prediction of the uncalibrated classifier. Parameters ---------- X : array-like, shape (n_samples, n_features) The samples. Returns ------- C : array, shape (n_samples,) The predicted class. """ check_is_fitted(self, ["classes_", "calibrated_classifiers_"]) return self.classes_[np.argmax(self.predict_proba(X), axis=1)] class _CalibratedClassifier(object): """Probability calibration with isotonic regression or sigmoid. It assumes that base_estimator has already been fit, and trains the calibration on the input set of the fit function. Note that this class should not be used as an estimator directly. Use CalibratedClassifierCV with cv="prefit" instead. Parameters ---------- base_estimator : instance BaseEstimator The classifier whose output decision function needs to be calibrated to offer more accurate predict_proba outputs. No default value since it has to be an already fitted estimator. method : 'sigmoid' | 'isotonic' 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. classes : array-like, shape (n_classes,), optional Contains unique classes used to fit the base estimator. if None, then classes is extracted from the given target values in fit(). References ---------- .. [1] Obtaining calibrated probability estimates from decision trees and naive Bayesian classifiers, B. Zadrozny & C. Elkan, ICML 2001 .. [2] Transforming Classifier Scores into Accurate Multiclass Probability Estimates, B. Zadrozny & C. Elkan, (KDD 2002) .. [3] Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods, J. Platt, (1999) .. [4] Predicting Good Probabilities with Supervised Learning, A. Niculescu-Mizil & R. Caruana, ICML 2005 """ def __init__(self, base_estimator, method='sigmoid', classes=None): self.base_estimator = base_estimator self.method = method self.classes = classes def _preproc(self, X): n_classes = len(self.classes_) if hasattr(self.base_estimator, "decision_function"): df = self.base_estimator.decision_function(X) if df.ndim == 1: df = df[:, np.newaxis] elif hasattr(self.base_estimator, "predict_proba"): df = self.base_estimator.predict_proba(X) if n_classes == 2: df = df[:, 1:] else: raise RuntimeError('classifier has no decision_function or ' 'predict_proba method.') idx_pos_class = self.label_encoder_.\ transform(self.base_estimator.classes_) return df, idx_pos_class def fit(self, X, y, sample_weight=None): """Calibrate the fitted model Parameters ---------- X : array-like, shape (n_samples, n_features) Training data. y : array-like, shape (n_samples,) Target values. sample_weight : array-like, shape = [n_samples] or None Sample weights. If None, then samples are equally weighted. Returns ------- self : object Returns an instance of self. """ self.label_encoder_ = LabelEncoder() if self.classes is None: self.label_encoder_.fit(y) else: self.label_encoder_.fit(self.classes) self.classes_ = self.label_encoder_.classes_ Y = label_binarize(y, self.classes_) df, idx_pos_class = self._preproc(X) self.calibrators_ = [] for k, this_df in zip(idx_pos_class, df.T): if self.method == 'isotonic': calibrator = IsotonicRegression(out_of_bounds='clip') elif self.method == 'sigmoid': calibrator = _SigmoidCalibration() else: raise ValueError('method should be "sigmoid" or ' '"isotonic". Got %s.' % self.method) calibrator.fit(this_df, Y[:, k], sample_weight) self.calibrators_.append(calibrator) return self def predict_proba(self, X): """Posterior probabilities of classification This function returns posterior probabilities of classification according to each class on an array of test vectors X. Parameters ---------- X : array-like, shape (n_samples, n_features) The samples. Returns ------- C : array, shape (n_samples, n_classes) The predicted probas. Can be exact zeros. """ n_classes = len(self.classes_) proba = np.zeros((X.shape[0], n_classes)) df, idx_pos_class = self._preproc(X) for k, this_df, calibrator in \ zip(idx_pos_class, df.T, self.calibrators_): if n_classes == 2: k += 1 proba[:, k] = calibrator.predict(this_df) # 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(df, y, sample_weight=None): """Probability Calibration with sigmoid method (Platt 2000) Parameters ---------- df : ndarray, shape (n_samples,) The decision function or predict proba for the samples. y : ndarray, shape (n_samples,) The targets. sample_weight : array-like, shape = [n_samples] or 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" """ df = column_or_1d(df) y = column_or_1d(y) F = df # F follows Platt's notations tiny = np.finfo(np.float).tiny # to avoid division by 0 warning # 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) E = np.exp(AB[0] * F + AB[1]) P = 1. / (1. + E) l = -(T * np.log(P + tiny) + T1 * np.log(1. - P + tiny)) if sample_weight is not None: return (sample_weight * l).sum() else: return l.sum() def grad(AB): # gradient of the objective function E = np.exp(AB[0] * F + AB[1]) P = 1. / (1. + E) TEP_minus_T1P = P * (T * E - T1) 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(BaseEstimator, RegressorMixin): """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, shape (n_samples,) Training data. y : array-like, shape (n_samples,) Training target. sample_weight : array-like, shape = [n_samples] or 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, shape (n_samples,) Data to predict from. Returns ------- T_ : array, shape (n_samples,) The predicted data. """ T = column_or_1d(T) return 1. / (1. + np.exp(self.a_ * T + self.b_)) def calibration_curve(y_true, y_prob, normalize=False, n_bins=5): """Compute true and predicted probabilities for a calibration curve. Calibration curves may also be referred to as reliability diagrams. Read more in the :ref:`User Guide `. Parameters ---------- y_true : array, shape (n_samples,) True targets. y_prob : array, shape (n_samples,) Probabilities of the positive class. normalize : bool, optional, default=False Whether y_prob needs to be normalized into the bin [0, 1], i.e. is not a proper probability. If True, the smallest value in y_prob is mapped onto 0 and the largest one onto 1. n_bins : int Number of bins. A bigger number requires more data. Returns ------- prob_true : array, shape (n_bins,) The true probability in each bin (fraction of positives). prob_pred : array, shape (n_bins,) 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). """ y_true = column_or_1d(y_true) y_prob = column_or_1d(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.") y_true = _check_binary_probabilistic_predictions(y_true, y_prob) bins = np.linspace(0., 1. + 1e-8, n_bins + 1) 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