
.. 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 <sphx_glr_download_auto_examples_model_selection_plot_precision_recall.py>`
        to download the full example code.

.. 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 the fraction of relevant items among actually returned items while recall
is a measure of the fraction of items that were returned among all items that should
have been returned. 'Relevancy' here refers to items that are
positively labeled, i.e., true positives and false negatives.

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}

The precision-recall curve shows the tradeoff between precision and
recall for different thresholds. A high area under the curve represents
both high recall and high precision. High precision is achieved by having
few false positives in the returned results, and high recall is achieved by
having few false negatives in the relevant results.
High scores for both show that the classifier is returning
accurate results (high precision), as well as returning a majority of all relevant
results (high recall).

A system with high recall but low precision returns most of the relevant items, but
the proportion of returned results that are incorrectly labeled is high. A
system with high precision but low recall is just the opposite, returning very
few of the relevant items, but most of its predicted labels are correct when compared
to the actual labels. An ideal system with high precision and high recall will
return most of the relevant items, with most results labeled correctly.

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. Changing the classifier threshold can only
change the numerator, :math:`T_p`. 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. Thus, precision does not necessarily
decrease with recall.

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_f_measure_metrics>`.

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 (:ref:`micro-averaging <average>`).

.. 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 94-98

.. code-block:: Python


    # Authors: The scikit-learn developers
    # SPDX-License-Identifier: BSD-3-Clause








.. GENERATED FROM PYTHON SOURCE LINES 99-106

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 106-123

.. 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 124-127

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 127-134

.. 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))
    classifier.fit(X_train, y_train)






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    </style><body><div id="sk-container-id-38" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),
                    (&#x27;linearsvc&#x27;,
                     LinearSVC(random_state=RandomState(MT19937) at 0x7877B8F6B840))])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item sk-dashed-wrapped"><div class="sk-label-container"><div class="sk-label fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-126" type="checkbox" ><label for="sk-estimator-id-126" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>Pipeline</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.7/modules/generated/sklearn.pipeline.Pipeline.html">?<span>Documentation for Pipeline</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted" data-param-prefix="">
            <div class="estimator-table">
                <details>
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.. GENERATED FROM PYTHON SOURCE LINES 135-147

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 147-154

.. code-block:: Python

    from sklearn.metrics import PrecisionRecallDisplay

    display = PrecisionRecallDisplay.from_estimator(
        classifier, X_test, y_test, name="LinearSVC", plot_chance_level=True, despine=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 155-158

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 158-165

.. code-block:: Python

    y_score = classifier.decision_function(X_test)

    display = PrecisionRecallDisplay.from_predictions(
        y_test, y_score, name="LinearSVC", plot_chance_level=True, despine=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 166-177

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 177-189

.. 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 190-192

We use :class:`~sklearn.multiclass.OneVsRestClassifier` for multi-label
prediction.

.. GENERATED FROM PYTHON SOURCE LINES 192-201

.. code-block:: Python

    from sklearn.multiclass import OneVsRestClassifier

    classifier = OneVsRestClassifier(
        make_pipeline(StandardScaler(), LinearSVC(random_state=random_state))
    )
    classifier.fit(X_train, Y_train)
    y_score = classifier.decision_function(X_test)









.. GENERATED FROM PYTHON SOURCE LINES 202-204

The average precision score in multi-label settings
...................................................

.. GENERATED FROM PYTHON SOURCE LINES 204-220

.. 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 221-223

Plot the micro-averaged Precision-Recall curve
..............................................

.. GENERATED FROM PYTHON SOURCE LINES 223-234

.. 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, despine=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 235-237

Plot Precision-Recall curve for each class and iso-f1 curves
............................................................

.. GENERATED FROM PYTHON SOURCE LINES 237-280

.. 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, despine=True
        )

    # 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 0.533 seconds)


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.. only:: html

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      :download:`Download Python source code: plot_precision_recall.py <plot_precision_recall.py>`

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      :download:`Download zipped: plot_precision_recall.zip <plot_precision_recall.zip>`


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