.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/calibration/plot_compare_calibration.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_calibration_plot_compare_calibration.py: ======================================== Comparison of Calibration of Classifiers ======================================== Well calibrated classifiers are probabilistic classifiers for which the output of :term:`predict_proba` can be directly interpreted as a confidence level. For instance, a well calibrated (binary) classifier should classify the samples such that for the samples to which it gave a :term:`predict_proba` value close to 0.8, approximately 80% actually belong to the positive class. In this example we will compare the calibration of four different models: :ref:`Logistic_regression`, :ref:`gaussian_naive_bayes`, :ref:`Random Forest Classifier ` and :ref:`Linear SVM `. .. GENERATED FROM PYTHON SOURCE LINES 20-31 Author: Jan Hendrik Metzen License: BSD 3 clause. Dataset ------- We will use a synthetic binary classification dataset with 100,000 samples and 20 features. Of the 20 features, only 2 are informative, 2 are redundant (random combinations of the informative features) and the remaining 16 are uninformative (random numbers). Of the 100,000 samples, 100 will be used for model fitting and the remaining for testing. .. GENERATED FROM PYTHON SOURCE LINES 31-47 .. code-block:: default from sklearn.datasets import make_classification from sklearn.model_selection import train_test_split X, y = make_classification( n_samples=100_000, n_features=20, n_informative=2, n_redundant=2, random_state=42 ) train_samples = 100 # Samples used for training the models X_train, X_test, y_train, y_test = train_test_split( X, y, shuffle=False, test_size=100_000 - train_samples, ) .. GENERATED FROM PYTHON SOURCE LINES 48-59 Calibration curves ------------------ Below, we train each of the four models with the small training dataset, then plot calibration curves (also known as reliability diagrams) using predicted probabilities of the test dataset. Calibration curves are created by binning predicted probabilities, then plotting the mean predicted probability in each bin against the observed frequency ('fraction of positives'). Below the calibration curve, we plot a histogram showing the distribution of the predicted probabilities or more specifically, the number of samples in each predicted probability bin. .. GENERATED FROM PYTHON SOURCE LINES 59-85 .. code-block:: default import numpy as np from sklearn.svm import LinearSVC class NaivelyCalibratedLinearSVC(LinearSVC): """LinearSVC with `predict_proba` method that naively scales `decision_function` output.""" def fit(self, X, y): super().fit(X, y) df = self.decision_function(X) self.df_min_ = df.min() self.df_max_ = df.max() def predict_proba(self, X): """Min-max scale output of `decision_function` to [0,1].""" df = self.decision_function(X) calibrated_df = (df - self.df_min_) / (self.df_max_ - self.df_min_) proba_pos_class = np.clip(calibrated_df, 0, 1) proba_neg_class = 1 - proba_pos_class proba = np.c_[proba_neg_class, proba_pos_class] return proba .. GENERATED FROM PYTHON SOURCE LINES 86-105 .. code-block:: default from sklearn.calibration import CalibrationDisplay from sklearn.ensemble import RandomForestClassifier from sklearn.linear_model import LogisticRegression from sklearn.naive_bayes import GaussianNB # Create classifiers lr = LogisticRegression() gnb = GaussianNB() svc = NaivelyCalibratedLinearSVC(C=1.0) rfc = RandomForestClassifier() clf_list = [ (lr, "Logistic"), (gnb, "Naive Bayes"), (svc, "SVC"), (rfc, "Random forest"), ] .. GENERATED FROM PYTHON SOURCE LINES 106-150 .. code-block:: default import matplotlib.pyplot as plt from matplotlib.gridspec import GridSpec fig = plt.figure(figsize=(10, 10)) gs = GridSpec(4, 2) colors = plt.cm.get_cmap("Dark2") ax_calibration_curve = fig.add_subplot(gs[:2, :2]) calibration_displays = {} for i, (clf, name) in enumerate(clf_list): clf.fit(X_train, y_train) display = CalibrationDisplay.from_estimator( clf, X_test, y_test, n_bins=10, name=name, ax=ax_calibration_curve, color=colors(i), ) calibration_displays[name] = display ax_calibration_curve.grid() ax_calibration_curve.set_title("Calibration plots") # Add histogram grid_positions = [(2, 0), (2, 1), (3, 0), (3, 1)] for i, (_, name) in enumerate(clf_list): row, col = grid_positions[i] ax = fig.add_subplot(gs[row, col]) ax.hist( calibration_displays[name].y_prob, range=(0, 1), bins=10, label=name, color=colors(i), ) ax.set(title=name, xlabel="Mean predicted probability", ylabel="Count") plt.tight_layout() plt.show() .. image-sg:: /auto_examples/calibration/images/sphx_glr_plot_compare_calibration_001.png :alt: Calibration plots, Logistic, Naive Bayes, SVC, Random forest :srcset: /auto_examples/calibration/images/sphx_glr_plot_compare_calibration_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 151-209 :class:`~sklearn.linear_model.LogisticRegression` returns well calibrated predictions as it directly optimizes log-loss. In contrast, the other methods return biased probabilities, with different biases for each method: * :class:`~sklearn.naive_bayes.GaussianNB` tends to push probabilities to 0 or 1 (see histogram). This is mainly because the naive Bayes equation only provides correct estimate of probabilities when the assumption that features are conditionally independent holds [2]_. However, features tend to be positively correlated and is the case with this dataset, which contains 2 features generated as random linear combinations of the informative features. These correlated features are effectively being 'counted twice', resulting in pushing the predicted probabilities towards 0 and 1 [3]_. * :class:`~sklearn.ensemble.RandomForestClassifier` shows the opposite behavior: the histograms show peaks at approx. 0.2 and 0.9 probability, while probabilities close to 0 or 1 are very rare. An explanation for this is given by Niculescu-Mizil and Caruana [1]_: "Methods such as bagging and random forests that average predictions from a base set of models can have difficulty making predictions near 0 and 1 because variance in the underlying base models will bias predictions that should be near zero or one away from these values. Because predictions are restricted to the interval [0,1], errors caused by variance tend to be one- sided near zero and one. For example, if a model should predict p = 0 for a case, the only way bagging can achieve this is if all bagged trees predict zero. If we add noise to the trees that bagging is averaging over, this noise will cause some trees to predict values larger than 0 for this case, thus moving the average prediction of the bagged ensemble away from 0. We observe this effect most strongly with random forests because the base-level trees trained with random forests have relatively high variance due to feature subsetting." As a result, the calibration curve shows a characteristic sigmoid shape, indicating that the classifier is under-confident and could return probabilities closer to 0 or 1. * To show the performance of :class:`~sklearn.svm.LinearSVC`, we naively scale the output of the :term:`decision_function` into [0, 1] by applying min-max scaling, since SVC does not output probabilities by default. :class:`~sklearn.svm.LinearSVC` shows an even more sigmoid curve than the :class:`~sklearn.ensemble.RandomForestClassifier`, which is typical for maximum-margin methods [1]_ as they focus on difficult to classify samples that are close to the decision boundary (the support vectors). References ---------- .. [1] `Predicting Good Probabilities with Supervised Learning `_, A. Niculescu-Mizil & R. Caruana, ICML 2005 .. [2] `Beyond independence: Conditions for the optimality of the simple bayesian classifier `_ Domingos, P., & Pazzani, M., Proc. 13th Intl. Conf. Machine Learning. 1996. .. [3] `Obtaining calibrated probability estimates from decision trees and naive Bayesian classifiers `_ Zadrozny, Bianca, and Charles Elkan. Icml. Vol. 1. 2001. .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 1.242 seconds) .. _sphx_glr_download_auto_examples_calibration_plot_compare_calibration.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.0.X?urlpath=lab/tree/notebooks/auto_examples/calibration/plot_compare_calibration.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_compare_calibration.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_compare_calibration.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_