.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/plot_quantile_mlpregression.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_plot_quantile_mlpregression.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_plot_quantile_mlpregression.py:


Quantile MLPRegressor
=====================

`scikit-learn <http://scikit-learn.org/stable/>`_ does not have a
quantile regression for multi-layer perceptron.
`mlinsights <https://sdpython.github.io/doc/dev/mlinsights/>`_
implements a version of it based on the *scikit-learn* model. The
implementation overwrites method ``_backprop``.

We first generate some dummy data.

.. GENERATED FROM PYTHON SOURCE LINES 13-28

.. code-block:: Python


    import numpy
    from pandas import DataFrame
    import matplotlib.pyplot as plt
    from sklearn.neural_network import MLPRegressor
    from mlinsights.mlmodel import QuantileMLPRegressor


    X = numpy.random.random(1000)
    eps1 = (numpy.random.random(900) - 0.5) * 0.1
    eps2 = (numpy.random.random(100)) * 10
    eps = numpy.hstack([eps1, eps2])
    X = X.reshape((1000, 1))
    Y = X.ravel() * 3.4 + 5.6 + eps








.. GENERATED FROM PYTHON SOURCE LINES 30-35

.. code-block:: Python



    clr = MLPRegressor(hidden_layer_sizes=(30,), activation="tanh")
    clr.fit(X, Y)






.. raw:: html

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    </style><div id="sk-container-id-1" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>MLPRegressor(activation=&#x27;tanh&#x27;, hidden_layer_sizes=(30,))</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"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-1" type="checkbox" checked><label for="sk-estimator-id-1" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>MLPRegressor</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/dev/modules/generated/sklearn.neural_network.MLPRegressor.html">?<span>Documentation for MLPRegressor</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted"><pre>MLPRegressor(activation=&#x27;tanh&#x27;, hidden_layer_sizes=(30,))</pre></div> </div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 37-42

.. code-block:: Python



    clq = QuantileMLPRegressor(hidden_layer_sizes=(30,), activation="tanh")
    clq.fit(X, Y)






.. raw:: html

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      text-align: left;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-2 div.sk-toggleable__content.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-2 div.sk-toggleable__content pre {
      margin: 0.2em;
      border-radius: 0.25em;
      color: var(--sklearn-color-text);
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-2 div.sk-toggleable__content.fitted pre {
      /* unfitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {
      /* Expand drop-down */
      max-height: 200px;
      max-width: 100%;
      overflow: auto;
    }

    #sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {
      content: "▾";
    }

    /* Pipeline/ColumnTransformer-specific style */

    #sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator-specific style */

    /* Colorize estimator box */
    #sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    #sk-container-id-2 div.sk-label label.sk-toggleable__label,
    #sk-container-id-2 div.sk-label label {
      /* The background is the default theme color */
      color: var(--sklearn-color-text-on-default-background);
    }

    /* On hover, darken the color of the background */
    #sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    /* Label box, darken color on hover, fitted */
    #sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator label */

    #sk-container-id-2 div.sk-label label {
      font-family: monospace;
      font-weight: bold;
      display: inline-block;
      line-height: 1.2em;
    }

    #sk-container-id-2 div.sk-label-container {
      text-align: center;
    }

    /* Estimator-specific */
    #sk-container-id-2 div.sk-estimator {
      font-family: monospace;
      border: 1px dotted var(--sklearn-color-border-box);
      border-radius: 0.25em;
      box-sizing: border-box;
      margin-bottom: 0.5em;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-2 div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    /* on hover */
    #sk-container-id-2 div.sk-estimator:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-2 div.sk-estimator.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Specification for estimator info (e.g. "i" and "?") */

    /* Common style for "i" and "?" */

    .sk-estimator-doc-link,
    a:link.sk-estimator-doc-link,
    a:visited.sk-estimator-doc-link {
      float: right;
      font-size: smaller;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-background);
      border-radius: 1em;
      height: 1em;
      width: 1em;
      text-decoration: none !important;
      margin-left: 0.5em;
      text-align: center;
      /* unfitted */
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
      color: var(--sklearn-color-unfitted-level-1);
    }

    .sk-estimator-doc-link.fitted,
    a:link.sk-estimator-doc-link.fitted,
    a:visited.sk-estimator-doc-link.fitted {
      /* fitted */
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

    /* On hover */
    div.sk-estimator:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover,
    div.sk-label-container:hover .sk-estimator-doc-link:hover,
    .sk-estimator-doc-link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover,
    div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,
    .sk-estimator-doc-link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    /* Span, style for the box shown on hovering the info icon */
    .sk-estimator-doc-link span {
      display: none;
      z-index: 9999;
      position: relative;
      font-weight: normal;
      right: .2ex;
      padding: .5ex;
      margin: .5ex;
      width: min-content;
      min-width: 20ex;
      max-width: 50ex;
      color: var(--sklearn-color-text);
      box-shadow: 2pt 2pt 4pt #999;
      /* unfitted */
      background: var(--sklearn-color-unfitted-level-0);
      border: .5pt solid var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted span {
      /* fitted */
      background: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3);
    }

    .sk-estimator-doc-link:hover span {
      display: block;
    }

    /* "?"-specific style due to the `<a>` HTML tag */

    #sk-container-id-2 a.estimator_doc_link {
      float: right;
      font-size: 1rem;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-background);
      border-radius: 1rem;
      height: 1rem;
      width: 1rem;
      text-decoration: none;
      /* unfitted */
      color: var(--sklearn-color-unfitted-level-1);
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
    }

    #sk-container-id-2 a.estimator_doc_link.fitted {
      /* fitted */
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

    /* On hover */
    #sk-container-id-2 a.estimator_doc_link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    #sk-container-id-2 a.estimator_doc_link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
    }
    </style><div id="sk-container-id-2" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>QuantileMLPRegressor(activation=&#x27;tanh&#x27;, hidden_layer_sizes=(30,))</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"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-2" type="checkbox" checked><label for="sk-estimator-id-2" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>QuantileMLPRegressor</div></div><div><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></div></label><div class="sk-toggleable__content fitted"><pre>QuantileMLPRegressor(activation=&#x27;tanh&#x27;, hidden_layer_sizes=(30,))</pre></div> </div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 44-50

.. code-block:: Python



    data = dict(X=X.ravel(), Y=Y, clr=clr.predict(X), clq=clq.predict(X))
    df = DataFrame(data)
    df.head()






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>X</th>
          <th>Y</th>
          <th>clr</th>
          <th>clq</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.379957</td>
          <td>6.937997</td>
          <td>7.492150</td>
          <td>6.949007</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.076410</td>
          <td>5.860495</td>
          <td>6.348967</td>
          <td>5.788681</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.292278</td>
          <td>6.559855</td>
          <td>7.178483</td>
          <td>6.630396</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.755102</td>
          <td>8.211254</td>
          <td>8.671232</td>
          <td>8.156544</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.637990</td>
          <td>7.733815</td>
          <td>8.331789</td>
          <td>7.806592</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 52-66

.. code-block:: Python



    fig, ax = plt.subplots(1, 1, figsize=(10, 4))
    choice = numpy.random.choice(X.shape[0] - 1, size=100)
    xx = X.ravel()[choice]
    yy = Y[choice]
    ax.plot(xx, yy, ".", label="data")
    xx = numpy.array([[0], [1]])
    y1 = clr.predict(xx)
    y2 = clq.predict(xx)
    ax.plot(xx, y1, "--", label="L2")
    ax.plot(xx, y2, "--", label="L1")
    ax.set_title("Quantile (L1) vs Square (L2) for MLPRegressor")
    ax.legend()



.. image-sg:: /auto_examples/images/sphx_glr_plot_quantile_mlpregression_001.png
   :alt: Quantile (L1) vs Square (L2) for MLPRegressor
   :srcset: /auto_examples/images/sphx_glr_plot_quantile_mlpregression_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x7f75565b6c80>




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

   **Total running time of the script:** (0 minutes 1.405 seconds)


.. _sphx_glr_download_auto_examples_plot_quantile_mlpregression.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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