.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/model_selection/plot_precision_recall.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via JupyterLite or Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_model_selection_plot_precision_recall.py: ================ Precision-Recall ================ Example of Precision-Recall metric to evaluate classifier output quality. Precision-Recall is a useful measure of success of prediction when the classes are very imbalanced. In information retrieval, precision is a measure of result relevancy, while recall is a measure of how many truly relevant results are returned. The precision-recall curve shows the tradeoff between precision and recall for different threshold. A high area under the curve represents both high recall and high precision, where high precision relates to a low false positive rate, and high recall relates to a low false negative rate. High scores for both show that the classifier is returning accurate results (high precision), as well as returning a majority of all positive results (high recall). A system with high recall but low precision returns many results, but most of its predicted labels are incorrect when compared to the training labels. A system with high precision but low recall is just the opposite, returning very few results, but most of its predicted labels are correct when compared to the training labels. An ideal system with high precision and high recall will return many results, with all results labeled correctly. Precision (:math:`P`) is defined as the number of true positives (:math:`T_p`) over the number of true positives plus the number of false positives (:math:`F_p`). :math:`P = \frac{T_p}{T_p+F_p}` Recall (:math:`R`) is defined as the number of true positives (:math:`T_p`) over the number of true positives plus the number of false negatives (:math:`F_n`). :math:`R = \frac{T_p}{T_p + F_n}` These quantities are also related to the :math:`F_1` score, which is the harmonic mean of precision and recall. Thus, we can compute the :math:`F_1` using the following formula: :math:`F_1 = \frac{2T_p}{2T_p + F_p + F_n}` Note that the precision may not decrease with recall. The definition of precision (:math:`\frac{T_p}{T_p + F_p}`) shows that lowering the threshold of a classifier may increase the denominator, by increasing the number of results returned. If the threshold was previously set too high, the new results may all be true positives, which will increase precision. If the previous threshold was about right or too low, further lowering the threshold will introduce false positives, decreasing precision. Recall is defined as :math:`\frac{T_p}{T_p+F_n}`, where :math:`T_p+F_n` does not depend on the classifier threshold. This means that lowering the classifier threshold may increase recall, by increasing the number of true positive results. It is also possible that lowering the threshold may leave recall unchanged, while the precision fluctuates. The relationship between recall and precision can be observed in the stairstep area of the plot - at the edges of these steps a small change in the threshold considerably reduces precision, with only a minor gain in recall. **Average precision** (AP) summarizes such a plot as the weighted mean of precisions achieved at each threshold, with the increase in recall from the previous threshold used as the weight: :math:`\text{AP} = \sum_n (R_n - R_{n-1}) P_n` where :math:`P_n` and :math:`R_n` are the precision and recall at the nth threshold. A pair :math:`(R_k, P_k)` is referred to as an *operating point*. AP and the trapezoidal area under the operating points (:func:`sklearn.metrics.auc`) are common ways to summarize a precision-recall curve that lead to different results. Read more in the :ref:`User Guide `. Precision-recall curves are typically used in binary classification to study the output of a classifier. In order to extend the precision-recall curve and average precision to multi-class or multi-label classification, it is necessary to binarize the output. One curve can be drawn per label, but one can also draw a precision-recall curve by considering each element of the label indicator matrix as a binary prediction (micro-averaging). .. note:: See also :func:`sklearn.metrics.average_precision_score`, :func:`sklearn.metrics.recall_score`, :func:`sklearn.metrics.precision_score`, :func:`sklearn.metrics.f1_score` .. GENERATED FROM PYTHON SOURCE LINES 96-103 In binary classification settings --------------------------------- Dataset and model ................. We will use a Linear SVC classifier to differentiate two types of irises. .. GENERATED FROM PYTHON SOURCE LINES 103-120 .. code-block:: Python import numpy as np from sklearn.datasets import load_iris from sklearn.model_selection import train_test_split X, y = load_iris(return_X_y=True) # Add noisy features random_state = np.random.RandomState(0) n_samples, n_features = X.shape X = np.concatenate([X, random_state.randn(n_samples, 200 * n_features)], axis=1) # Limit to the two first classes, and split into training and test X_train, X_test, y_train, y_test = train_test_split( X[y < 2], y[y < 2], test_size=0.5, random_state=random_state ) .. GENERATED FROM PYTHON SOURCE LINES 121-124 Linear SVC will expect each feature to have a similar range of values. Thus, we will first scale the data using a :class:`~sklearn.preprocessing.StandardScaler`. .. GENERATED FROM PYTHON SOURCE LINES 124-133 .. code-block:: Python from sklearn.pipeline import make_pipeline from sklearn.preprocessing import StandardScaler from sklearn.svm import LinearSVC classifier = make_pipeline( StandardScaler(), LinearSVC(random_state=random_state, dual="auto") ) classifier.fit(X_train, y_train) .. raw:: html 
Pipeline(steps=[('standardscaler', StandardScaler()),
                    ('linearsvc',
                     LinearSVC(dual='auto',
                               random_state=RandomState(MT19937) at 0x7FDEBF5D0140))])
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.. GENERATED FROM PYTHON SOURCE LINES 134-146 Plot the Precision-Recall curve ............................... To plot the precision-recall curve, you should use :class:`~sklearn.metrics.PrecisionRecallDisplay`. Indeed, there is two methods available depending if you already computed the predictions of the classifier or not. Let's first plot the precision-recall curve without the classifier predictions. We use :func:`~sklearn.metrics.PrecisionRecallDisplay.from_estimator` that computes the predictions for us before plotting the curve. .. GENERATED FROM PYTHON SOURCE LINES 146-153 .. code-block:: Python from sklearn.metrics import PrecisionRecallDisplay display = PrecisionRecallDisplay.from_estimator( classifier, X_test, y_test, name="LinearSVC", plot_chance_level=True ) _ = display.ax_.set_title("2-class Precision-Recall curve") .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_001.png :alt: 2-class Precision-Recall curve :srcset: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 154-157 If we already got the estimated probabilities or scores for our model, then we can use :func:`~sklearn.metrics.PrecisionRecallDisplay.from_predictions`. .. GENERATED FROM PYTHON SOURCE LINES 157-164 .. code-block:: Python y_score = classifier.decision_function(X_test) display = PrecisionRecallDisplay.from_predictions( y_test, y_score, name="LinearSVC", plot_chance_level=True ) _ = display.ax_.set_title("2-class Precision-Recall curve") .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_002.png :alt: 2-class Precision-Recall curve :srcset: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 165-176 In multi-label settings ----------------------- The precision-recall curve does not support the multilabel setting. However, one can decide how to handle this case. We show such an example below. Create multi-label data, fit, and predict ......................................... We create a multi-label dataset, to illustrate the precision-recall in multi-label settings. .. GENERATED FROM PYTHON SOURCE LINES 176-188 .. code-block:: Python from sklearn.preprocessing import label_binarize # Use label_binarize to be multi-label like settings Y = label_binarize(y, classes=[0, 1, 2]) n_classes = Y.shape[1] # Split into training and test X_train, X_test, Y_train, Y_test = train_test_split( X, Y, test_size=0.5, random_state=random_state ) .. GENERATED FROM PYTHON SOURCE LINES 189-191 We use :class:`~sklearn.multiclass.OneVsRestClassifier` for multi-label prediction. .. GENERATED FROM PYTHON SOURCE LINES 191-200 .. code-block:: Python from sklearn.multiclass import OneVsRestClassifier classifier = OneVsRestClassifier( make_pipeline(StandardScaler(), LinearSVC(random_state=random_state, dual="auto")) ) classifier.fit(X_train, Y_train) y_score = classifier.decision_function(X_test) .. GENERATED FROM PYTHON SOURCE LINES 201-203 The average precision score in multi-label settings ................................................... .. GENERATED FROM PYTHON SOURCE LINES 203-219 .. code-block:: Python from sklearn.metrics import average_precision_score, precision_recall_curve # For each class precision = dict() recall = dict() average_precision = dict() for i in range(n_classes): precision[i], recall[i], _ = precision_recall_curve(Y_test[:, i], y_score[:, i]) average_precision[i] = average_precision_score(Y_test[:, i], y_score[:, i]) # A "micro-average": quantifying score on all classes jointly precision["micro"], recall["micro"], _ = precision_recall_curve( Y_test.ravel(), y_score.ravel() ) average_precision["micro"] = average_precision_score(Y_test, y_score, average="micro") .. GENERATED FROM PYTHON SOURCE LINES 220-222 Plot the micro-averaged Precision-Recall curve .............................................. .. GENERATED FROM PYTHON SOURCE LINES 222-233 .. code-block:: Python from collections import Counter display = PrecisionRecallDisplay( recall=recall["micro"], precision=precision["micro"], average_precision=average_precision["micro"], prevalence_pos_label=Counter(Y_test.ravel())[1] / Y_test.size, ) display.plot(plot_chance_level=True) _ = display.ax_.set_title("Micro-averaged over all classes") .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_003.png :alt: Micro-averaged over all classes :srcset: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 234-236 Plot Precision-Recall curve for each class and iso-f1 curves ............................................................ .. GENERATED FROM PYTHON SOURCE LINES 236-277 .. code-block:: Python from itertools import cycle import matplotlib.pyplot as plt # setup plot details colors = cycle(["navy", "turquoise", "darkorange", "cornflowerblue", "teal"]) _, ax = plt.subplots(figsize=(7, 8)) f_scores = np.linspace(0.2, 0.8, num=4) lines, labels = [], [] for f_score in f_scores: x = np.linspace(0.01, 1) y = f_score * x / (2 * x - f_score) (l,) = plt.plot(x[y >= 0], y[y >= 0], color="gray", alpha=0.2) plt.annotate("f1={0:0.1f}".format(f_score), xy=(0.9, y[45] + 0.02)) display = PrecisionRecallDisplay( recall=recall["micro"], precision=precision["micro"], average_precision=average_precision["micro"], ) display.plot(ax=ax, name="Micro-average precision-recall", color="gold") for i, color in zip(range(n_classes), colors): display = PrecisionRecallDisplay( recall=recall[i], precision=precision[i], average_precision=average_precision[i], ) display.plot(ax=ax, name=f"Precision-recall for class {i}", color=color) # add the legend for the iso-f1 curves handles, labels = display.ax_.get_legend_handles_labels() handles.extend([l]) labels.extend(["iso-f1 curves"]) # set the legend and the axes ax.legend(handles=handles, labels=labels, loc="best") ax.set_title("Extension of Precision-Recall curve to multi-class") plt.show() .. image-sg:: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_004.png :alt: Extension of Precision-Recall curve to multi-class :srcset: /auto_examples/model_selection/images/sphx_glr_plot_precision_recall_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.372 seconds) .. _sphx_glr_download_auto_examples_model_selection_plot_precision_recall.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.4.X?urlpath=lab/tree/notebooks/auto_examples/model_selection/plot_precision_recall.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/model_selection/plot_precision_recall.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_precision_recall.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_precision_recall.py ` .. include:: plot_precision_recall.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_