.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/neighbors/plot_digits_kde_sampling.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_neighbors_plot_digits_kde_sampling.py>`
        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_neighbors_plot_digits_kde_sampling.py:


=========================
Kernel Density Estimation
=========================

This example shows how kernel density estimation (KDE), a powerful
non-parametric density estimation technique, can be used to learn
a generative model for a dataset.  With this generative model in place,
new samples can be drawn.  These new samples reflect the underlying model
of the data.

.. GENERATED FROM PYTHON SOURCE LINES 13-68



.. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_digits_kde_sampling_001.png
   :alt: Selection from the input data, "New" digits drawn from the kernel density model
   :srcset: /auto_examples/neighbors/images/sphx_glr_plot_digits_kde_sampling_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    best bandwidth: 3.79269019073225






|

.. code-block:: Python


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

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import load_digits
    from sklearn.decomposition import PCA
    from sklearn.model_selection import GridSearchCV
    from sklearn.neighbors import KernelDensity

    # load the data
    digits = load_digits()

    # project the 64-dimensional data to a lower dimension
    pca = PCA(n_components=15, whiten=False)
    data = pca.fit_transform(digits.data)

    # use grid search cross-validation to optimize the bandwidth
    params = {"bandwidth": np.logspace(-1, 1, 20)}
    grid = GridSearchCV(KernelDensity(), params)
    grid.fit(data)

    print("best bandwidth: {0}".format(grid.best_estimator_.bandwidth))

    # use the best estimator to compute the kernel density estimate
    kde = grid.best_estimator_

    # sample 44 new points from the data
    new_data = kde.sample(44, random_state=0)
    new_data = pca.inverse_transform(new_data)

    # turn data into a 4x11 grid
    new_data = new_data.reshape((4, 11, -1))
    real_data = digits.data[:44].reshape((4, 11, -1))

    # plot real digits and resampled digits
    fig, ax = plt.subplots(9, 11, subplot_kw=dict(xticks=[], yticks=[]))
    for j in range(11):
        ax[4, j].set_visible(False)
        for i in range(4):
            im = ax[i, j].imshow(
                real_data[i, j].reshape((8, 8)), cmap=plt.cm.binary, interpolation="nearest"
            )
            im.set_clim(0, 16)
            im = ax[i + 5, j].imshow(
                new_data[i, j].reshape((8, 8)), cmap=plt.cm.binary, interpolation="nearest"
            )
            im.set_clim(0, 16)

    ax[0, 5].set_title("Selection from the input data")
    ax[5, 5].set_title('"New" digits drawn from the kernel density model')

    plt.show()


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

   **Total running time of the script:** (0 minutes 3.925 seconds)


.. _sphx_glr_download_auto_examples_neighbors_plot_digits_kde_sampling.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/main?urlpath=lab/tree/notebooks/auto_examples/neighbors/plot_digits_kde_sampling.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

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


.. include:: plot_digits_kde_sampling.recommendations


.. only:: html

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

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