.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples_classification/3-scientific-articles/plot_sadinle2019_example.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_examples_classification_3-scientific-articles_plot_sadinle2019_example.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_classification_3-scientific-articles_plot_sadinle2019_example.py:


================================================
Reproducing Example 7 from Sadinle et al. (2019)
================================================

We use :class:`~mapie.classification.MapieClassifier` to reproduce
Example 7 from Sadinle et al. (2019).

We consider a two-dimensional dataset with three labels. The distribution
of the data is a bivariate normal with diagonal covariance matrices for
each label.
We model the data with Gaussian Naive Bayes classifier
:class:`~sklearn.naive_bayes.GaussianNB` as a base model.

Prediction sets are estimated by :class:`~mapie.classification.MapieClassifier`
from the distribution of the softmax scores of the true labels for three
alpha values (0.2, 0.1, and 0.05) giving different class coverage levels.

When the class coverage level is not large enough, the prediction sets can be
empty.
This happens because the model is uncertain at the border between two labels.
These so-called null regions disappear for larger coverage levels.

.. GENERATED FROM PYTHON SOURCE LINES 24-98



.. image-sg:: /examples_classification/3-scientific-articles/images/sphx_glr_plot_sadinle2019_example_001.png
   :alt: Predicted labels, Number of labels for alpha=0.2, Number of labels for alpha=0.1, Number of labels for alpha=0.05
   :srcset: /examples_classification/3-scientific-articles/images/sphx_glr_plot_sadinle2019_example_001.png
   :class: sphx-glr-single-img





.. code-block:: default

    import matplotlib.pyplot as plt
    import numpy as np
    from sklearn.naive_bayes import GaussianNB

    from mapie.classification import MapieClassifier

    # Create training set from multivariate normal distribution
    centers = [(0, 3.5), (-2, 0), (2, 0)]
    # covs = [[[1, 0], [0, 1]], [[2, 0], [0, 2]], [[5, 0], [0, 1]]]
    covs = [np.eye(2), np.eye(2) * 2, np.diag([5, 1])]
    x_min, x_max, y_min, y_max, step = -6, 8, -6, 8, 0.1
    n_samples = 500
    n_classes = 3
    alpha = [0.2, 0.1, 0.05]
    np.random.seed(42)
    X_train = np.vstack(
        [
            np.random.multivariate_normal(center, cov, n_samples)
            for center, cov in zip(centers, covs)
        ]
    )
    y_train = np.hstack([np.full(n_samples, i) for i in range(n_classes)])


    # Create test from (x, y) coordinates
    xx, yy = np.meshgrid(
        np.arange(x_min, x_max, step), np.arange(x_min, x_max, step)
    )
    X_test = np.stack([xx.ravel(), yy.ravel()], axis=1)

    # Apply MapieClassifier on the dataset to get prediction sets
    clf = GaussianNB().fit(X_train, y_train)
    y_pred = clf.predict(X_test)
    y_pred_proba = clf.predict_proba(X_test)
    y_pred_proba_max = np.max(y_pred_proba, axis=1)
    mapie = MapieClassifier(estimator=clf, cv="prefit", method="lac")
    mapie.fit(X_train, y_train)
    y_pred_mapie, y_ps_mapie = mapie.predict(X_test, alpha=alpha)

    # Plot the results
    tab10 = plt.cm.get_cmap("Purples", 4)
    colors = {0: "#1f77b4", 1: "#ff7f0e", 2: "#2ca02c", 3: "#d62728"}
    y_pred_col = list(map(colors.get, y_pred_mapie))
    y_train_col = list(map(colors.get, y_train))
    y_train_col = [colors[int(i)] for _, i in enumerate(y_train)]
    fig, axs = plt.subplots(1, 4, figsize=(20, 4))
    axs[0].scatter(
        X_test[:, 0], X_test[:, 1], color=y_pred_col, marker=".", s=10, alpha=0.4
    )
    axs[0].scatter(
        X_train[:, 0],
        X_train[:, 1],
        color=y_train_col,
        marker="o",
        s=10,
        edgecolor="k",
    )
    axs[0].set_title("Predicted labels")
    for i, alpha_ in enumerate(alpha):
        y_ps_sums = y_ps_mapie[:, :, i].sum(axis=1)
        num_labels = axs[i + 1].scatter(
            X_test[:, 0],
            X_test[:, 1],
            c=y_ps_sums,
            marker=".",
            s=10,
            alpha=1,
            cmap=tab10,
            vmin=0,
            vmax=3,
        )
        cbar = plt.colorbar(num_labels, ax=axs[i + 1])
        axs[i + 1].set_title(f"Number of labels for alpha={alpha_}")
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.999 seconds)


.. _sphx_glr_download_examples_classification_3-scientific-articles_plot_sadinle2019_example.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: plot_sadinle2019_example.py <plot_sadinle2019_example.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: plot_sadinle2019_example.ipynb <plot_sadinle2019_example.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_