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Probability calibration of classifiers#
When performing classification you often want to predict not only the class label, but also the associated probability. This probability gives you some kind of confidence on the prediction. However, not all classifiers provide well-calibrated probabilities, some being over-confident while others being under-confident. Thus, a separate calibration of predicted probabilities is often desirable as a postprocessing. This example illustrates two different methods for this calibration and evaluates the quality of the returned probabilities using Brier’s score (see https://en.wikipedia.org/wiki/Brier_score).
Compared are the estimated probability using a Gaussian naive Bayes classifier without calibration, with a sigmoid calibration, and with a non-parametric isotonic calibration. One can observe that only the non-parametric model is able to provide a probability calibration that returns probabilities close to the expected 0.5 for most of the samples belonging to the middle cluster with heterogeneous labels. This results in a significantly improved Brier score.
# Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause
Generate synthetic dataset#
importnumpyasnp fromsklearn.datasetsimport make_blobs fromsklearn.model_selectionimport train_test_split n_samples = 50000 # Generate 3 blobs with 2 classes where the second blob contains # half positive samples and half negative samples. Probability in this # blob is therefore 0.5. centers = [(-5, -5), (0, 0), (5, 5)] X, y = make_blobs (n_samples=n_samples, centers=centers, shuffle=False, random_state=42) y[: n_samples // 2] = 0 y[n_samples // 2 :] = 1 sample_weight = np.random.RandomState (42).rand(y.shape[0]) # split train, test for calibration X_train, X_test, y_train, y_test, sw_train, sw_test = train_test_split ( X, y, sample_weight, test_size=0.9, random_state=42 )
Gaussian Naive-Bayes#
fromsklearn.calibrationimport CalibratedClassifierCV fromsklearn.metricsimport brier_score_loss fromsklearn.naive_bayesimport GaussianNB # With no calibration clf = GaussianNB () clf.fit(X_train, y_train) # GaussianNB itself does not support sample-weights prob_pos_clf = clf.predict_proba(X_test)[:, 1] # With isotonic calibration clf_isotonic = CalibratedClassifierCV (clf, cv=2, method="isotonic") clf_isotonic.fit(X_train, y_train, sample_weight=sw_train) prob_pos_isotonic = clf_isotonic.predict_proba(X_test)[:, 1] # With sigmoid calibration clf_sigmoid = CalibratedClassifierCV (clf, cv=2, method="sigmoid") clf_sigmoid.fit(X_train, y_train, sample_weight=sw_train) prob_pos_sigmoid = clf_sigmoid.predict_proba(X_test)[:, 1] print("Brier score losses: (the smaller the better)") clf_score = brier_score_loss (y_test, prob_pos_clf, sample_weight=sw_test) print("No calibration: %1.3f" % clf_score) clf_isotonic_score = brier_score_loss (y_test, prob_pos_isotonic, sample_weight=sw_test) print("With isotonic calibration: %1.3f" % clf_isotonic_score) clf_sigmoid_score = brier_score_loss (y_test, prob_pos_sigmoid, sample_weight=sw_test) print("With sigmoid calibration: %1.3f" % clf_sigmoid_score)
Brier score losses: (the smaller the better) No calibration: 0.104 With isotonic calibration: 0.084 With sigmoid calibration: 0.109
Plot data and the predicted probabilities#
importmatplotlib.pyplotasplt frommatplotlibimport cm plt.figure () y_unique = np.unique (y) colors = cm.rainbow(np.linspace (0.0, 1.0, y_unique.size)) for this_y, color in zip(y_unique, colors): this_X = X_train[y_train == this_y] this_sw = sw_train[y_train == this_y] plt.scatter ( this_X[:, 0], this_X[:, 1], s=this_sw * 50, c=color[np.newaxis , :], alpha=0.5, edgecolor="k", label="Class %s" % this_y, ) plt.legend (loc="best") plt.title ("Data") plt.figure () order = np.lexsort ((prob_pos_clf,)) plt.plot (prob_pos_clf[order], "r", label="No calibration (%1.3f)" % clf_score) plt.plot ( prob_pos_isotonic[order], "g", linewidth=3, label="Isotonic calibration (%1.3f)" % clf_isotonic_score, ) plt.plot ( prob_pos_sigmoid[order], "b", linewidth=3, label="Sigmoid calibration (%1.3f)" % clf_sigmoid_score, ) plt.plot ( np.linspace (0, y_test.size, 51)[1::2], y_test[order].reshape(25, -1).mean(1), "k", linewidth=3, label=r"Empirical", ) plt.ylim ([-0.05, 1.05]) plt.xlabel ("Instances sorted according to predicted probability (uncalibrated GNB)") plt.ylabel ("P(y=1)") plt.legend (loc="upper left") plt.title ("Gaussian naive Bayes probabilities") plt.show ()
- Data
- Gaussian naive Bayes probabilities
Total running time of the script: (0 minutes 0.379 seconds)
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