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

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

.. _sphx_glr_auto_examples_inspection_plot_partial_dependence_visualization_api.py:


=========================================
Advanced Plotting With Partial Dependence
=========================================
The :class:`~sklearn.inspection.PartialDependenceDisplay` object can be used
for plotting without needing to recalculate the partial dependence. In this
example, we show how to plot partial dependence plots and how to quickly
customize the plot with the visualization API.

.. note::

    See also :ref:`sphx_glr_auto_examples_miscellaneous_plot_roc_curve_visualization_api.py`

.. GENERATED FROM PYTHON SOURCE LINES 15-29

.. code-block:: Python


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

    import matplotlib.pyplot as plt
    import pandas as pd

    from sklearn.datasets import load_diabetes
    from sklearn.inspection import PartialDependenceDisplay
    from sklearn.neural_network import MLPRegressor
    from sklearn.pipeline import make_pipeline
    from sklearn.preprocessing import StandardScaler
    from sklearn.tree import DecisionTreeRegressor








.. GENERATED FROM PYTHON SOURCE LINES 30-35

Train models on the diabetes dataset
================================================

First, we train a decision tree and a multi-layer perceptron on the diabetes
dataset.

.. GENERATED FROM PYTHON SOURCE LINES 35-48

.. code-block:: Python


    diabetes = load_diabetes()
    X = pd.DataFrame(diabetes.data, columns=diabetes.feature_names)
    y = diabetes.target

    tree = DecisionTreeRegressor()
    mlp = make_pipeline(
        StandardScaler(),
        MLPRegressor(hidden_layer_sizes=(100, 100), tol=1e-2, max_iter=500, random_state=0),
    )
    tree.fit(X, y)
    mlp.fit(X, y)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>.sk-global {
      /* Definition of color scheme common for light and dark mode */
      --sklearn-color-text: #000;
      --sklearn-color-text-muted: #666;
      --sklearn-color-line: gray;
      /* Definition of color scheme for unfitted estimators */
      --sklearn-color-unfitted-level-0: #fff5e6;
      --sklearn-color-unfitted-level-1: #f6e4d2;
      --sklearn-color-unfitted-level-2: #ffe0b3;
      --sklearn-color-unfitted-level-3: chocolate;
      /* Definition of color scheme for fitted estimators */
      --sklearn-color-fitted-level-0: #f0f8ff;
      --sklearn-color-fitted-level-1: #d4ebff;
      --sklearn-color-fitted-level-2: #b3dbfd;
      --sklearn-color-fitted-level-3: cornflowerblue;
    }

    .sk-global.light {
      /* Specific color for light theme */
      --sklearn-color-text-on-default-background: black;
      --sklearn-color-background: white;
      --sklearn-color-border-box: black;
      --sklearn-color-icon: #696969;
    }

    .sk-global.dark {
      --sklearn-color-text-on-default-background: white;
      --sklearn-color-background: #111;
      --sklearn-color-border-box: white;
      --sklearn-color-icon: #878787;
    }

    .sk-global {
      color: var(--sklearn-color-text);
    }

    .sk-global pre {
      padding: 0;
    }

    .sk-global input.sk-hidden--visually {
      border: 0;
      clip-path: inset(100%);
      height: 1px;
      margin: -1px;
      overflow: hidden;
      padding: 0;
      position: absolute;
      width: 1px;
    }

    .sk-global div.sk-dashed-wrapped {
      border: 1px dashed var(--sklearn-color-line);
      margin: 0 0.4em 0.5em 0.4em;
      box-sizing: border-box;
      padding-bottom: 0.4em;
      background-color: var(--sklearn-color-background);
    }

    .sk-global div.sk-container {
      /* jupyter's `normalize.less` sets `[hidden] { display: none; }`
         but bootstrap.min.css set `[hidden] { display: none !important; }`
         so we also need the `!important` here to be able to override the
         default hidden behavior on the sphinx rendered scikit-learn.org.
         See: https://github.com/scikit-learn/scikit-learn/issues/21755 */
      display: inline-block !important;
      position: relative;
    }

    .sk-global div.sk-text-repr-fallback {
      display: none;
    }

    div.sk-parallel-item,
    div.sk-serial,
    div.sk-item {
      /* draw centered vertical line to link estimators */
      background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));
      background-size: 2px 100%;
      background-repeat: no-repeat;
      background-position: center center;
    }

    /* Parallel-specific style estimator block */

    .sk-global div.sk-parallel-item::after {
      content: "";
      width: 100%;
      border-bottom: 2px solid var(--sklearn-color-text-on-default-background);
      flex-grow: 1;
    }

    .sk-global div.sk-parallel {
      display: flex;
      align-items: stretch;
      justify-content: center;
      background-color: var(--sklearn-color-background);
      position: relative;
    }

    .sk-global div.sk-parallel-item {
      display: flex;
      flex-direction: column;
    }

    .sk-global div.sk-parallel-item:first-child::after {
      align-self: flex-end;
      width: 50%;
    }

    .sk-global div.sk-parallel-item:last-child::after {
      align-self: flex-start;
      width: 50%;
    }

    .sk-global div.sk-parallel-item:only-child::after {
      width: 0;
    }

    /* Serial-specific style estimator block */

    .sk-global div.sk-serial {
      display: flex;
      flex-direction: column;
      align-items: center;
      background-color: var(--sklearn-color-background);
      padding-right: 1em;
      padding-left: 1em;
    }


    /* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is
    clickable and can be expanded/collapsed.
    - Pipeline and ColumnTransformer use this feature and define the default style
    - Estimators will overwrite some part of the style using the `sk-estimator` class
    */

    /* Pipeline and ColumnTransformer style (default) */

    .sk-global div.sk-toggleable {
      /* Default theme specific background. It is overwritten whether we have a
      specific estimator or a Pipeline/ColumnTransformer */
      background-color: var(--sklearn-color-background);
    }

    /* Toggleable label */
    .sk-global label.sk-toggleable__label {
      cursor: pointer;
      display: flex;
      width: 100%;
      margin-bottom: 0;
      padding: 0.5em;
      box-sizing: border-box;
      text-align: center;
      align-items: center;
      justify-content: center;
      gap: 0.5em;
    }

    .sk-global label.sk-toggleable__label .caption {
      font-size: 0.6rem;
      font-weight: lighter;
      color: var(--sklearn-color-text-muted);
    }

    .sk-global label.sk-toggleable__label-arrow:before {
      /* Arrow on the left of the label */
      content: "▸";
      float: left;
      margin-right: 0.25em;
      color: var(--sklearn-color-icon);
    }

    .sk-global label.sk-toggleable__label-arrow:hover:before {
      color: var(--sklearn-color-text);
    }

    /* Toggleable content - dropdown */

    .sk-global div.sk-toggleable__content {
      display: none;
      text-align: left;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

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

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

    .sk-global input.sk-toggleable__control:checked~div.sk-toggleable__content {
      /* Expand drop-down */
      display: block;
      width: 100%;
      overflow: visible;
    }

    .sk-global input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {
      content: "▾";
    }

    /* Pipeline/ColumnTransformer-specific style */

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

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

    .sk-global div.sk-label label.sk-toggleable__label,
    .sk-global 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-global 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-global 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-global div.sk-label label {
      font-family: monospace;
      font-weight: bold;
      line-height: 1.2em;
    }

    .sk-global div.sk-label-container {
      text-align: center;
    }

    /* Estimator-specific */
    .sk-global 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-global div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

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

    .sk-global 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-unfitted-level-0);
      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-3) 1pt solid;
      color: var(--sklearn-color-unfitted-level-3);
    }

    .sk-estimator-doc-link.fitted,
    a:link.sk-estimator-doc-link.fitted,
    a:visited.sk-estimator-doc-link.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-3) 1pt solid;
      color: var(--sklearn-color-fitted-level-3);
    }

    /* 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);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-unfitted-level-0);
      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);
      border: var(--sklearn-color-fitted-level-0) 1pt solid;
      color: var(--sklearn-color-fitted-level-0);
      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-global a.estimator_doc_link {
      float: right;
      font-size: 1rem;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-unfitted-level-0);
      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-global a.estimator_doc_link.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

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

    .sk-global a.estimator_doc_link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
    }

    .sk-top-container.sk-global {
      /* pydata-sphinx-theme hides overflow, so scrolling is disabled.
       We need to set it to !important and add tabindex="0" in the HTML
       to allow keyboard-only users to navigate the display. */
      overflow-x: scroll !important;
      max-width: 100%;
    }

    .estimator-table {
        font-family: monospace;
    }

    .estimator-table summary {
        padding: .5rem;
        cursor: pointer;
    }

    .estimator-table summary::marker {
        font-size: 0.7rem;
    }

    .estimator-table details[open] {
        padding-left: 0.1rem;
        padding-right: 0.1rem;
        padding-bottom: 0.3rem;
    }

    .estimator-table .parameters-table {
        margin-left: auto !important;
        margin-right: auto !important;
        margin-top: 0;
    }

    .estimator-table .parameters-table tr:nth-child(odd) {
        background-color: #fff;
    }

    .estimator-table .parameters-table tr:nth-child(even) {
        background-color: #f6f6f6;
    }

    .estimator-table .parameters-table tr:hover td {
        background-color: #e0e0e0;
    }

    .estimator-table table :is(td, th) {
        border: 1px solid rgba(106, 105, 104, 0.232);
    }

    /*
        `table td`is set in notebook with right text-align.
        We need to overwrite it.
    */
    .estimator-table table td.param {
        text-align: left;
        position: relative;
        padding: 0;
    }

    .user-set td {
        color:rgb(255, 94, 0);
        text-align: left !important;
    }

    .user-set td.value {
        color:rgb(255, 94, 0);
        background-color: transparent;
    }

    .default td, .estimator-table th {
        color: black;
        text-align: left !important;
    }

    .user-set td i,
    .default td i {
        color: black;
    }

    td.fitted-att-type {
        white-space: preserve nowrap;
    }

    /*
        Styles for parameter documentation links
        We need styling for visited so jupyter doesn't overwrite it
    */
    a.param-doc-link,
    a.param-doc-link:link,
    a.param-doc-link:visited {
        text-decoration: underline dashed;
        text-underline-offset: .3em;
        color: inherit;
        display: block;
        padding: .5em;
    }

    @supports(anchor-name: --doc-link) {
        a.param-doc-link,
        a.param-doc-link:link,
        a.param-doc-link:visited {
        anchor-name: --doc-link;
        }
    }

    /* "hack" to make the entire area of the cell containing the link clickable */
    a.param-doc-link::before {
        position: absolute;
        content: "";
        inset: 0;
    }

    .param-doc-description {
        display: none;
        position: absolute;
        z-index: 9999;
        left: 0;
        padding: .5ex;
        margin-left: 1.5em;
        color: var(--sklearn-color-text);
        box-shadow: .3em .3em .4em #999;
        width: max-content;
        text-align: left;
        max-height: 10em;
        overflow-y: auto;

        /* unfitted */
        background: var(--sklearn-color-unfitted-level-0);
        border: thin solid var(--sklearn-color-unfitted-level-3);
    }

    @supports(position-area: center right) {
        .param-doc-description {
        position-area: center right;
        position: fixed;
        margin-left: 0;
        }
    }

    /* Fitted state for parameter tooltips */
    .fitted .param-doc-description {
        /* fitted */
        background: var(--sklearn-color-fitted-level-0);
        border: thin solid var(--sklearn-color-fitted-level-3);
    }

    .param-doc-link:hover .param-doc-description {
        display: block;
    }

    .copy-paste-icon {
        background-image: url(data:image/svg+xml;base64,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);
        background-repeat: no-repeat;
        background-size: 14px 14px;
        background-position: 0;
        display: inline-block;
        width: 14px;
        height: 14px;
        cursor: pointer;
    }

    .features {
      font-family: monospace;
      cursor: pointer;
      background-color: var(--sklearn-color-unfitted-level-0);
      border: 1px dotted var(--sklearn-color-border-box);
      border-radius: .20em;
      margin-bottom: 0.5em;
      font-size: inherit; /* Needed for jupyter */
    }

    .features.fitted {
      background-color: var(--sklearn-color-fitted-level-0);
    }

    .features summary {
      cursor: pointer;
      display: flex;
      margin-bottom: 0;
      text-align: center;
      align-items: center;
      justify-content: center;
      gap: 0.5em;
      padding: .25em;
    }

    .features details[open] > summary {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
      border-radius: .20em 0 0 0;
    }

    .features.fitted details[open] > summary {
      background-color: var(--sklearn-color-fitted-level-2);
      border-radius: .20em 0 0 0;
    }

    .features details > summary .arrow::before {
      content: "▸";
      color: grey;
    }

    .features details[open] > summary .arrow::before {
      content: "▾";
    }

    .features details:hover > summary {
      margin: 0;
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    .features.fitted details:hover > summary {
      margin: 0;
      background-color: var(--sklearn-color-fitted-level-2);
    }

    .features .features-container {
      max-width: 15em;
      max-height: 10em;
      overflow: auto;
      scrollbar-width: thin;
      padding: .25em 0.1rem;
      background-color: var(--sklearn-color-unfitted-level-0);
      border-radius: 0 0 .5em .5em;
    }

    .features.fitted .features-container {
      background-color: var(--sklearn-color-fitted-level-0);
    }

    .features .image-container {
      block-size: 1em;
      inline-size: 1em;
      padding: 0;
      margin: 0%;
      display: flex;
      justify-content: center;
      align-items: center;
    }

    .features .copy-paste-icon {
      background-size: 1em 1em;
      width: 1em;
      height: 1em;
      filter: grayscale(100%) opacity(60%);
    }

    .features .features-container table {
      width: 100%;
      margin: 0.01em;
    }

    .features .features-container table tr:nth-child(odd) {
      background-color: #fff;
    }

    .features .features-container table tr:nth-child(even) {
      background-color: #f6f6f6;
    }

    .features .features-container table tr:hover {
      background-color: #e0e0e0;
    }

    .features .features-container table {
      table-layout: inherit;
    }

    .features .features-container table td {
      text-align: left;
      padding: 0 0.5em;
      border: 1px solid rgba(106, 105, 104, 0.232);
      white-space: nowrap;
      color: var(--sklearn-color-text);
    }

    .total_features {
      display: flex;
      justify-content: center;
      margin-top: 0.5em;
    }
    </style><body><div id="sk-container-id-25" tabindex="0" class="sk-top-container sk-global"><div class="sk-text-repr-fallback"><pre>Pipeline(steps=[(&#x27;standardscaler&#x27;, StandardScaler()),
                    (&#x27;mlpregressor&#x27;,
                     MLPRegressor(hidden_layer_sizes=(100, 100), max_iter=500,
                                  random_state=0, tol=0.01))])</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 sk-global" id="sk-estimator-id-75" type="checkbox" ><label for="sk-estimator-id-75" 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/1.9/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>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('steps',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-steps;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=steps,-list%20of%20tuples">
                steps
                <span class="param-doc-description"
                style="position-anchor: --doc-link-steps;">
                steps: list of tuples<br><br>List of (name of step, estimator) tuples that are to be chained in<br>sequential order. To be compatible with the scikit-learn API, all steps<br>must define `fit`. All non-last steps must also define `transform`. See<br>:ref:`Combining Estimators &lt;combining_estimators&gt;` for more details.</span>
            </a>
        </td>
                <td class="value">[(&#x27;standardscaler&#x27;, ...), (&#x27;mlpregressor&#x27;, ...)]</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('transform_input',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-transform_input;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=transform_input,-list%20of%20str%2C%20default%3DNone">
                transform_input
                <span class="param-doc-description"
                style="position-anchor: --doc-link-transform_input;">
                transform_input: list of str, default=None<br><br>The names of the :term:`metadata` parameters that should be transformed by the<br>pipeline before passing it to the step consuming it.<br><br>This enables transforming some input arguments to ``fit`` (other than ``X``)<br>to be transformed by the steps of the pipeline up to the step which requires<br>them. Requirement is defined via :ref:`metadata routing &lt;metadata_routing&gt;`.<br>For instance, this can be used to pass a validation set through the pipeline.<br><br>You can only set this if metadata routing is enabled, which you<br>can enable using ``sklearn.set_config(enable_metadata_routing=True)``.<br><br>.. versionadded:: 1.6</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('memory',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-memory;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=memory,-str%20or%20object%20with%20the%20joblib.Memory%20interface%2C%20default%3DNone">
                memory
                <span class="param-doc-description"
                style="position-anchor: --doc-link-memory;">
                memory: str or object with the joblib.Memory interface, default=None<br><br>Used to cache the fitted transformers of the pipeline. The last step<br>will never be cached, even if it is a transformer. By default, no<br>caching is performed. If a string is given, it is the path to the<br>caching directory. Enabling caching triggers a clone of the transformers<br>before fitting. Therefore, the transformer instance given to the<br>pipeline cannot be inspected directly. Use the attribute ``named_steps``<br>or ``steps`` to inspect estimators within the pipeline. Caching the<br>transformers is advantageous when fitting is time consuming. See<br>:ref:`sphx_glr_auto_examples_neighbors_plot_caching_nearest_neighbors.py`<br>for an example on how to enable caching.</span>
            </a>
        </td>
                <td class="value">None</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('verbose',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-verbose;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=verbose,-bool%2C%20default%3DFalse">
                verbose
                <span class="param-doc-description"
                style="position-anchor: --doc-link-verbose;">
                verbose: bool, default=False<br><br>If True, the time elapsed while fitting each step will be printed as it<br>is completed.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
    
            <div class="estimator-table">
                <details>
                    <summary>Fitted attributes</summary>
                    <table class="parameters-table">
                        <tbody>
                            <tr>
                            <th>Name</th>
                            <th>Type</th>
                            <th>Value</th>
                            </tr>
                        
           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-feature_names_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=feature_names_in_,-ndarray%20of%20shape%20%28n_features_in_%2C%29">
                feature_names_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-feature_names_in_;">
                feature_names_in_: ndarray of shape (`n_features_in_`,)<br><br>Names of features seen during :term:`fit`. Only defined if the<br>underlying estimator exposes such an attribute when fit.<br><br>.. versionadded:: 1.0</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[object](10,)</td>
               <td>[&#x27;age&#x27;,&#x27;sex&#x27;,&#x27;bmi&#x27;,...,&#x27;s4&#x27;,&#x27;s5&#x27;,&#x27;s6&#x27;]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_features_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.pipeline.Pipeline.html#:~:text=n_features_in_,-int">
                n_features_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_features_in_;">
                n_features_in_: int<br><br>Number of features seen during :term:`fit`. Only defined if the<br>underlying first estimator in `steps` exposes such an attribute<br>when fit.<br><br>.. versionadded:: 0.24</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>10</td>


           </tr>
    
                        </tbody>
                    </table>
                </details>
            </div>
        </div></div></div><div class="sk-serial"><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually sk-global" id="sk-estimator-id-76" type="checkbox" ><label for="sk-estimator-id-76" class="sk-toggleable__label fitted sk-toggleable__label-arrow"><div><div>StandardScaler</div></div><div><a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html">?<span>Documentation for StandardScaler</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="standardscaler__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('copy',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-copy;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=copy,-bool%2C%20default%3DTrue">
                copy
                <span class="param-doc-description"
                style="position-anchor: --doc-link-copy;">
                copy: bool, default=True<br><br>If False, try to avoid a copy and do inplace scaling instead.<br>This is not guaranteed to always work inplace; e.g. if the data is<br>not a NumPy array or scipy.sparse CSR matrix, a copy may still be<br>returned.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('with_mean',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-with_mean;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=with_mean,-bool%2C%20default%3DTrue">
                with_mean
                <span class="param-doc-description"
                style="position-anchor: --doc-link-with_mean;">
                with_mean: bool, default=True<br><br>If True, center the data before scaling.<br>This does not work (and will raise an exception) when attempted on<br>sparse matrices, because centering them entails building a dense<br>matrix which in common use cases is likely to be too large to fit in<br>memory.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('with_std',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-with_std;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=with_std,-bool%2C%20default%3DTrue">
                with_std
                <span class="param-doc-description"
                style="position-anchor: --doc-link-with_std;">
                with_std: bool, default=True<br><br>If True, scale the data to unit variance (or equivalently,<br>unit standard deviation).</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
    
            <div class="estimator-table">
                <details>
                    <summary>Fitted attributes</summary>
                    <table class="parameters-table">
                        <tbody>
                            <tr>
                            <th>Name</th>
                            <th>Type</th>
                            <th>Value</th>
                            </tr>
                        
           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-feature_names_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=feature_names_in_,-ndarray%20of%20shape%20%28n_features_in_%2C%29">
                feature_names_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-feature_names_in_;">
                feature_names_in_: ndarray of shape (`n_features_in_`,)<br><br>Names of features seen during :term:`fit`. Defined only when `X`<br>has feature names that are all strings.<br><br>.. versionadded:: 1.0</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[object](10,)</td>
               <td>[&#x27;age&#x27;,&#x27;sex&#x27;,&#x27;bmi&#x27;,...,&#x27;s4&#x27;,&#x27;s5&#x27;,&#x27;s6&#x27;]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-mean_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=mean_,-ndarray%20of%20shape%20%28n_features%2C%29%20or%20None">
                mean_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-mean_;">
                mean_: ndarray of shape (n_features,) or None<br><br>The mean value for each feature in the training set.<br>Equal to ``None`` when ``with_mean=False`` and ``with_std=False``.</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](10,)</td>
               <td>[-0., 0.,-0.,...,-0., 0., 0.]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_features_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=n_features_in_,-int">
                n_features_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_features_in_;">
                n_features_in_: int<br><br>Number of features seen during :term:`fit`.<br><br>.. versionadded:: 0.24</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>10</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_samples_seen_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=n_samples_seen_,-int%20or%20ndarray%20of%20shape%20%28n_features%2C%29">
                n_samples_seen_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_samples_seen_;">
                n_samples_seen_: int or ndarray of shape (n_features,)<br><br>The number of samples processed by the estimator for each feature.<br>If there are no missing samples, the ``n_samples_seen`` will be an<br>integer, otherwise it will be an array of dtype int. If<br>`sample_weights` are used it will be a float (if no missing data)<br>or an array of dtype float that sums the weights seen so far.<br>Will be reset on new calls to fit, but increments across<br>``partial_fit`` calls.</span>
            </a>
        </td>
               <td class="fitted-att-type">float64</td>
               <td>442</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-scale_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=scale_,-ndarray%20of%20shape%20%28n_features%2C%29%20or%20None">
                scale_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-scale_;">
                scale_: ndarray of shape (n_features,) or None<br><br>Per feature relative scaling of the data to achieve zero mean and unit<br>variance. Generally this is calculated using `np.sqrt(var_)`. If a<br>variance is zero, we can&#x27;t achieve unit variance, and the data is left<br>as-is, giving a scaling factor of 1. `scale_` is equal to `None`<br>when `with_std=False`.<br><br>.. versionadded:: 0.17<br>   *scale_*</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](10,)</td>
               <td>[0.05,0.05,0.05,...,0.05,0.05,0.05]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-var_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.preprocessing.StandardScaler.html#:~:text=var_,-ndarray%20of%20shape%20%28n_features%2C%29%20or%20None">
                var_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-var_;">
                var_: ndarray of shape (n_features,) or None<br><br>The variance for each feature in the training set. Used to compute<br>`scale_`. Equal to ``None`` when ``with_mean=False`` and<br>``with_std=False``.</span>
            </a>
        </td>
               <td class="fitted-att-type">ndarray[float64](10,)</td>
               <td>[0.,0.,0.,...,0.,0.,0.]</td>


           </tr>
    
                        </tbody>
                    </table>
                </details>
            </div>
        </div></div></div>
            <div class="features fitted">
              <details>
                <summary>
                  <div class="arrow"></div>
                  <div>10 features</div>
                  <div class="image-container" title="Copy all output features">
                    <i class="copy-paste-icon"
                      onclick="
                      event.stopPropagation();
                      event.preventDefault();
                      copyFeatureNamesToClipboard(this);
                      "
                    >
                    </i>
                  </div>
                </summary>
                <div class="features-container">
                    <table class="features-table">
                      <tbody>
                    
            <tr>
              <td>age</td>
            </tr>

    
            <tr>
              <td>sex</td>
            </tr>

    
            <tr>
              <td>bmi</td>
            </tr>

    
            <tr>
              <td>bp</td>
            </tr>

    
            <tr>
              <td>s1</td>
            </tr>

    
            <tr>
              <td>s2</td>
            </tr>

    
            <tr>
              <td>s3</td>
            </tr>

    
            <tr>
              <td>s4</td>
            </tr>

    
            <tr>
              <td>s5</td>
            </tr>

    
            <tr>
              <td>s6</td>
            </tr>

    
                      </tbody>
                    </table>
                </div>
              </details>
            </div>
        <div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually sk-global" id="sk-estimator-id-77" type="checkbox" ><label for="sk-estimator-id-77" 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/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html">?<span>Documentation for MLPRegressor</span></a></div></label><div class="sk-toggleable__content fitted" data-param-prefix="mlpregressor__">
            <div class="estimator-table">
                <details>
                    <summary>Parameters</summary>
                    <table class="parameters-table">
                      <tbody>
                    
            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('hidden_layer_sizes',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-hidden_layer_sizes;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=hidden_layer_sizes,-array-like%20of%20shape%28n_layers%20-%202%2C%29%2C%20default%3D%28100%2C%29">
                hidden_layer_sizes
                <span class="param-doc-description"
                style="position-anchor: --doc-link-hidden_layer_sizes;">
                hidden_layer_sizes: array-like of shape(n_layers - 2,), default=(100,)<br><br>The ith element represents the number of neurons in the ith<br>hidden layer.</span>
            </a>
        </td>
                <td class="value">(100, ...)</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_iter',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-max_iter;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=max_iter,-int%2C%20default%3D200">
                max_iter
                <span class="param-doc-description"
                style="position-anchor: --doc-link-max_iter;">
                max_iter: int, default=200<br><br>Maximum number of iterations. The solver iterates until convergence<br>(determined by &#x27;tol&#x27;) or this number of iterations. For stochastic<br>solvers (&#x27;sgd&#x27;, &#x27;adam&#x27;), note that this determines the number of epochs<br>(how many times each data point will be used), not the number of<br>gradient steps.</span>
            </a>
        </td>
                <td class="value">500</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('random_state',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-random_state;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=random_state,-int%2C%20RandomState%20instance%2C%20default%3DNone">
                random_state
                <span class="param-doc-description"
                style="position-anchor: --doc-link-random_state;">
                random_state: int, RandomState instance, default=None<br><br>Determines random number generation for weights and bias<br>initialization, train-test split if early stopping is used, and batch<br>sampling when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.<br>Pass an int for reproducible results across multiple function calls.<br>See :term:`Glossary &lt;random_state&gt;`.</span>
            </a>
        </td>
                <td class="value">0</td>
            </tr>
    

            <tr class="user-set">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('tol',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-tol;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=tol,-float%2C%20default%3D1e-4">
                tol
                <span class="param-doc-description"
                style="position-anchor: --doc-link-tol;">
                tol: float, default=1e-4<br><br>Tolerance for the optimization. When the loss or score is not improving<br>by at least ``tol`` for ``n_iter_no_change`` consecutive iterations,<br>unless ``learning_rate`` is set to &#x27;adaptive&#x27;, convergence is<br>considered to be reached and training stops.</span>
            </a>
        </td>
                <td class="value">0.01</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('loss',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-loss;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=loss,-%7B%27squared_error%27%2C%20%27poisson%27%7D%2C%20default%3D%27squared_error%27">
                loss
                <span class="param-doc-description"
                style="position-anchor: --doc-link-loss;">
                loss: {&#x27;squared_error&#x27;, &#x27;poisson&#x27;}, default=&#x27;squared_error&#x27;<br><br>The loss function to use when training the weights. Note that the<br>&quot;squared error&quot; and &quot;poisson&quot; losses actually implement<br>&quot;half squares error&quot; and &quot;half poisson deviance&quot; to simplify the<br>computation of the gradient. Furthermore, the &quot;poisson&quot; loss internally uses<br>a log-link (exponential as the output activation function) and requires<br>``y &gt;= 0``.<br><br>.. versionchanged:: 1.7<br>   Added parameter `loss` and option &#x27;poisson&#x27;.</span>
            </a>
        </td>
                <td class="value">&#x27;squared_error&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('activation',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-activation;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=activation,-%7B%27identity%27%2C%20%27logistic%27%2C%20%27tanh%27%2C%20%27relu%27%7D%2C%20default%3D%27relu%27">
                activation
                <span class="param-doc-description"
                style="position-anchor: --doc-link-activation;">
                activation: {&#x27;identity&#x27;, &#x27;logistic&#x27;, &#x27;tanh&#x27;, &#x27;relu&#x27;}, default=&#x27;relu&#x27;<br><br>Activation function for the hidden layer.<br><br>- &#x27;identity&#x27;, no-op activation, useful to implement linear bottleneck,<br>  returns f(x) = x<br><br>- &#x27;logistic&#x27;, the logistic sigmoid function,<br>  returns f(x) = 1 / (1 + exp(-x)).<br><br>- &#x27;tanh&#x27;, the hyperbolic tan function,<br>  returns f(x) = tanh(x).<br><br>- &#x27;relu&#x27;, the rectified linear unit function,<br>  returns f(x) = max(0, x)</span>
            </a>
        </td>
                <td class="value">&#x27;relu&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('solver',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-solver;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=solver,-%7B%27lbfgs%27%2C%20%27sgd%27%2C%20%27adam%27%7D%2C%20default%3D%27adam%27">
                solver
                <span class="param-doc-description"
                style="position-anchor: --doc-link-solver;">
                solver: {&#x27;lbfgs&#x27;, &#x27;sgd&#x27;, &#x27;adam&#x27;}, default=&#x27;adam&#x27;<br><br>The solver for weight optimization.<br><br>- &#x27;lbfgs&#x27; is an optimizer in the family of quasi-Newton methods.<br><br>- &#x27;sgd&#x27; refers to stochastic gradient descent.<br><br>- &#x27;adam&#x27; refers to a stochastic gradient-based optimizer proposed by<br>  Kingma, Diederik, and Jimmy Ba<br><br>For a comparison between Adam optimizer and SGD, see<br>:ref:`sphx_glr_auto_examples_neural_networks_plot_mlp_training_curves.py`.<br><br>Note: The default solver &#x27;adam&#x27; works pretty well on relatively<br>large datasets (with thousands of training samples or more) in terms of<br>both training time and validation score.<br>For small datasets, however, &#x27;lbfgs&#x27; can converge faster and perform<br>better.</span>
            </a>
        </td>
                <td class="value">&#x27;adam&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('alpha',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-alpha;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=alpha,-float%2C%20default%3D0.0001">
                alpha
                <span class="param-doc-description"
                style="position-anchor: --doc-link-alpha;">
                alpha: float, default=0.0001<br><br>Strength of the L2 regularization term. The L2 regularization term<br>is divided by the sample size when added to the loss.</span>
            </a>
        </td>
                <td class="value">0.0001</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('batch_size',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-batch_size;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=batch_size,-int%2C%20default%3D%27auto%27">
                batch_size
                <span class="param-doc-description"
                style="position-anchor: --doc-link-batch_size;">
                batch_size: int, default=&#x27;auto&#x27;<br><br>Size of minibatches for stochastic optimizers.<br>If the solver is &#x27;lbfgs&#x27;, the regressor will not use minibatch.<br>When set to &quot;auto&quot;, `batch_size=min(200, n_samples)`.</span>
            </a>
        </td>
                <td class="value">&#x27;auto&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('learning_rate',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-learning_rate;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=learning_rate,-%7B%27constant%27%2C%20%27invscaling%27%2C%20%27adaptive%27%7D%2C%20default%3D%27constant%27">
                learning_rate
                <span class="param-doc-description"
                style="position-anchor: --doc-link-learning_rate;">
                learning_rate: {&#x27;constant&#x27;, &#x27;invscaling&#x27;, &#x27;adaptive&#x27;}, default=&#x27;constant&#x27;<br><br>Learning rate schedule for weight updates.<br><br>- &#x27;constant&#x27; is a constant learning rate given by<br>  &#x27;learning_rate_init&#x27;.<br><br>- &#x27;invscaling&#x27; gradually decreases the learning rate ``learning_rate_``<br>  at each time step &#x27;t&#x27; using an inverse scaling exponent of &#x27;power_t&#x27;.<br>  effective_learning_rate = learning_rate_init / pow(t, power_t)<br><br>- &#x27;adaptive&#x27; keeps the learning rate constant to<br>  &#x27;learning_rate_init&#x27; as long as training loss keeps decreasing.<br>  Each time two consecutive epochs fail to decrease training loss by at<br>  least tol, or fail to increase validation score by at least tol if<br>  &#x27;early_stopping&#x27; is on, the current learning rate is divided by 5.<br><br>Only used when solver=&#x27;sgd&#x27;.</span>
            </a>
        </td>
                <td class="value">&#x27;constant&#x27;</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('learning_rate_init',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-learning_rate_init;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=learning_rate_init,-float%2C%20default%3D0.001">
                learning_rate_init
                <span class="param-doc-description"
                style="position-anchor: --doc-link-learning_rate_init;">
                learning_rate_init: float, default=0.001<br><br>The initial learning rate used. It controls the step-size<br>in updating the weights. Only used when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
                <td class="value">0.001</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('power_t',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-power_t;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=power_t,-float%2C%20default%3D0.5">
                power_t
                <span class="param-doc-description"
                style="position-anchor: --doc-link-power_t;">
                power_t: float, default=0.5<br><br>The exponent for inverse scaling learning rate.<br>It is used in updating effective learning rate when the learning_rate<br>is set to &#x27;invscaling&#x27;. Only used when solver=&#x27;sgd&#x27;.</span>
            </a>
        </td>
                <td class="value">0.5</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('shuffle',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-shuffle;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=shuffle,-bool%2C%20default%3DTrue">
                shuffle
                <span class="param-doc-description"
                style="position-anchor: --doc-link-shuffle;">
                shuffle: bool, default=True<br><br>Whether to shuffle samples in each iteration. Only used when<br>solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('verbose',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-verbose;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=verbose,-bool%2C%20default%3DFalse">
                verbose
                <span class="param-doc-description"
                style="position-anchor: --doc-link-verbose;">
                verbose: bool, default=False<br><br>Whether to print progress messages to stdout.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('warm_start',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-warm_start;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=warm_start,-bool%2C%20default%3DFalse">
                warm_start
                <span class="param-doc-description"
                style="position-anchor: --doc-link-warm_start;">
                warm_start: bool, default=False<br><br>When set to True, reuse the solution of the previous<br>call to fit as initialization, otherwise, just erase the<br>previous solution. See :term:`the Glossary &lt;warm_start&gt;`.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('momentum',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-momentum;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=momentum,-float%2C%20default%3D0.9">
                momentum
                <span class="param-doc-description"
                style="position-anchor: --doc-link-momentum;">
                momentum: float, default=0.9<br><br>Momentum for gradient descent update. Should be between 0 and 1. Only<br>used when solver=&#x27;sgd&#x27;.</span>
            </a>
        </td>
                <td class="value">0.9</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('nesterovs_momentum',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-nesterovs_momentum;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=nesterovs_momentum,-bool%2C%20default%3DTrue">
                nesterovs_momentum
                <span class="param-doc-description"
                style="position-anchor: --doc-link-nesterovs_momentum;">
                nesterovs_momentum: bool, default=True<br><br>Whether to use Nesterov&#x27;s momentum. Only used when solver=&#x27;sgd&#x27; and<br>momentum &gt; 0.</span>
            </a>
        </td>
                <td class="value">True</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('early_stopping',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-early_stopping;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=early_stopping,-bool%2C%20default%3DFalse">
                early_stopping
                <span class="param-doc-description"
                style="position-anchor: --doc-link-early_stopping;">
                early_stopping: bool, default=False<br><br>Whether to use early stopping to terminate training when validation<br>score is not improving. If set to True, it will automatically set<br>aside ``validation_fraction`` of training data as validation and<br>terminate training when validation score is not improving by at<br>least ``tol`` for ``n_iter_no_change`` consecutive epochs.<br>Only effective when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
                <td class="value">False</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('validation_fraction',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-validation_fraction;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=validation_fraction,-float%2C%20default%3D0.1">
                validation_fraction
                <span class="param-doc-description"
                style="position-anchor: --doc-link-validation_fraction;">
                validation_fraction: float, default=0.1<br><br>The proportion of training data to set aside as validation set for<br>early stopping. Must be between 0 and 1.<br>Only used if early_stopping is True.</span>
            </a>
        </td>
                <td class="value">0.1</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('beta_1',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-beta_1;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=beta_1,-float%2C%20default%3D0.9">
                beta_1
                <span class="param-doc-description"
                style="position-anchor: --doc-link-beta_1;">
                beta_1: float, default=0.9<br><br>Exponential decay rate for estimates of first moment vector in adam,<br>should be in [0, 1). Only used when solver=&#x27;adam&#x27;.</span>
            </a>
        </td>
                <td class="value">0.9</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('beta_2',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-beta_2;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=beta_2,-float%2C%20default%3D0.999">
                beta_2
                <span class="param-doc-description"
                style="position-anchor: --doc-link-beta_2;">
                beta_2: float, default=0.999<br><br>Exponential decay rate for estimates of second moment vector in adam,<br>should be in [0, 1). Only used when solver=&#x27;adam&#x27;.</span>
            </a>
        </td>
                <td class="value">0.999</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('epsilon',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-epsilon;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=epsilon,-float%2C%20default%3D1e-8">
                epsilon
                <span class="param-doc-description"
                style="position-anchor: --doc-link-epsilon;">
                epsilon: float, default=1e-8<br><br>Value for numerical stability in adam. Only used when solver=&#x27;adam&#x27;.</span>
            </a>
        </td>
                <td class="value">1e-08</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('n_iter_no_change',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_iter_no_change;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=n_iter_no_change,-int%2C%20default%3D10">
                n_iter_no_change
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_iter_no_change;">
                n_iter_no_change: int, default=10<br><br>Maximum number of epochs to not meet ``tol`` improvement.<br>Only effective when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.<br><br>.. versionadded:: 0.20</span>
            </a>
        </td>
                <td class="value">10</td>
            </tr>
    

            <tr class="default">
                <td><i class="copy-paste-icon"
                     onclick="copyToClipboard('max_fun',
                              this.parentElement.nextElementSibling)"
                ></i></td>
                <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-max_fun;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=max_fun,-int%2C%20default%3D15000">
                max_fun
                <span class="param-doc-description"
                style="position-anchor: --doc-link-max_fun;">
                max_fun: int, default=15000<br><br>Only used when solver=&#x27;lbfgs&#x27;. Maximum number of function calls.<br>The solver iterates until convergence (determined by ``tol``), number<br>of iterations reaches max_iter, or this number of function calls.<br>Note that number of function calls will be greater than or equal to<br>the number of iterations for the MLPRegressor.<br><br>.. versionadded:: 0.22</span>
            </a>
        </td>
                <td class="value">15000</td>
            </tr>
    
                      </tbody>
                    </table>
                </details>
            </div>
    
            <div class="estimator-table">
                <details>
                    <summary>Fitted attributes</summary>
                    <table class="parameters-table">
                        <tbody>
                            <tr>
                            <th>Name</th>
                            <th>Type</th>
                            <th>Value</th>
                            </tr>
                        
           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-best_loss_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=best_loss_,-float">
                best_loss_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-best_loss_;">
                best_loss_: float<br><br>The minimum loss reached by the solver throughout fitting.<br>If `early_stopping=True`, this attribute is set to `None`. Refer to<br>the `best_validation_score_` fitted attribute instead.<br>Only accessible when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
               <td class="fitted-att-type">float64</td>
               <td>1110</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-best_validation_score_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=best_validation_score_,-float%20or%20None">
                best_validation_score_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-best_validation_score_;">
                best_validation_score_: float or None<br><br>The best validation score (i.e. R2 score) that triggered the<br>early stopping. Only available if `early_stopping=True`, otherwise the<br>attribute is set to `None`.<br>Only accessible when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
               <td class="fitted-att-type">NoneType</td>
               <td>None</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-coefs_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=coefs_,-list%20of%20shape%20%28n_layers%20-%201%2C%29">
                coefs_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-coefs_;">
                coefs_: list of shape (n_layers - 1,)<br><br>The ith element in the list represents the weight matrix corresponding<br>to layer i.</span>
            </a>
        </td>
               <td class="fitted-att-type">list</td>
               <td>[array([[ 2.26...1628603e-01]]), array([[ 0.16...pe=(100, 100)), array([[ 0.22... 0.43165108]])]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-intercepts_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=intercepts_,-list%20of%20shape%20%28n_layers%20-%201%2C%29">
                intercepts_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-intercepts_;">
                intercepts_: list of shape (n_layers - 1,)<br><br>The ith element in the list represents the bias vector corresponding to<br>layer i + 1.</span>
            </a>
        </td>
               <td class="fitted-att-type">list</td>
               <td>[array([ 0.369...  0.27554867]), array([ 0.313...  0.03395789]), array([0.3372181])]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-loss_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=loss_,-float">
                loss_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-loss_;">
                loss_: float<br><br>The current loss computed with the loss function.</span>
            </a>
        </td>
               <td class="fitted-att-type">float64</td>
               <td>1110</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-loss_curve_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=loss_curve_,-list%20of%20shape%20%28n_iter_%2C%29">
                loss_curve_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-loss_curve_;">
                loss_curve_: list of shape (`n_iter_`,)<br><br>Loss value evaluated at the end of each training step.<br>The ith element in the list represents the loss at the ith iteration.<br>Only accessible when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
               <td class="fitted-att-type">list</td>
               <td>[np.float64(14432.825030436637), np.float64(14372.921005126946), np.float64(14311.387710317184), np.float64(14245.964671913125), ...]</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_features_in_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=n_features_in_,-int">
                n_features_in_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_features_in_;">
                n_features_in_: int<br><br>Number of features seen during :term:`fit`.<br><br>.. versionadded:: 0.24</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>10</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_iter_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=n_iter_,-int">
                n_iter_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_iter_;">
                n_iter_: int<br><br>The number of iterations the solver has run.</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>500</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_layers_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=n_layers_,-int">
                n_layers_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_layers_;">
                n_layers_: int<br><br>Number of layers.</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>4</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-n_outputs_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=n_outputs_,-int">
                n_outputs_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-n_outputs_;">
                n_outputs_: int<br><br>Number of outputs.</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>1</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-out_activation_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=out_activation_,-str">
                out_activation_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-out_activation_;">
                out_activation_: str<br><br>Name of the output activation function.</span>
            </a>
        </td>
               <td class="fitted-att-type">str</td>
               <td>&#x27;id...ty&#x27;</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-t_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=t_,-int">
                t_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-t_;">
                t_: int<br><br>The number of training samples seen by the solver during fitting.<br>Mathematically equals `n_iters * X.shape[0]`, it means<br>`time_step` and it is used by optimizer&#x27;s learning rate scheduler.</span>
            </a>
        </td>
               <td class="fitted-att-type">int</td>
               <td>221000</td>


           </tr>
    

           <tr class="default">
               <td class="param">
            <a class="param-doc-link"
                style="anchor-name: --doc-link-validation_scores_;"
                rel="noreferrer" target="_blank" href="https://scikit-learn.org/1.9/modules/generated/sklearn.neural_network.MLPRegressor.html#:~:text=validation_scores_,-list%20of%20shape%20%28n_iter_%2C%29%20or%20None">
                validation_scores_
                <span class="param-doc-description"
                style="position-anchor: --doc-link-validation_scores_;">
                validation_scores_: list of shape (`n_iter_`,) or None<br><br>The score at each iteration on a held-out validation set. The score<br>reported is the R2 score. Only available if `early_stopping=True`,<br>otherwise the attribute is set to `None`.<br>Only accessible when solver=&#x27;sgd&#x27; or &#x27;adam&#x27;.</span>
            </a>
        </td>
               <td class="fitted-att-type">NoneType</td>
               <td>None</td>


           </tr>
    
                        </tbody>
                    </table>
                </details>
            </div>
        </div></div></div></div></div></div></div><script>/*  Authors: The scikit-learn developers
     SPDX-License-Identifier: BSD-3-Clause
    */

    function copyToClipboard(text, element) {
        // Get the parameter prefix from the closest toggleable content
        const toggleableContent = element.closest('.sk-toggleable__content');
        const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';
        const fullParamName = paramPrefix ? `${paramPrefix}${text}` : text;

        const originalStyle = element.style;
        const computedStyle = window.getComputedStyle(element);
        const originalWidth = computedStyle.width;
        const originalHTML = element.innerHTML.replace('Copied!', '');

        navigator.clipboard.writeText(fullParamName)
            .then(() => {
                element.style.width = originalWidth;
                element.style.color = 'green';
                element.innerHTML = "Copied!";

                setTimeout(() => {
                    element.innerHTML = originalHTML;
                    element.style = originalStyle;
                }, 2000);
            })
            .catch(err => {
                console.error('Failed to copy:', err);
                element.style.color = 'red';
                element.innerHTML = "Failed!";
                setTimeout(() => {
                    element.innerHTML = originalHTML;
                    element.style = originalStyle;
                }, 2000);
            });
        return false;
    }

    document.querySelectorAll('.copy-paste-icon').forEach(function(element) {
        const toggleableContent = element.closest('.sk-toggleable__content');
        const paramPrefix = toggleableContent ? toggleableContent.dataset.paramPrefix : '';

        const parent = element.parentElement;
        if (!parent || !parent.nextElementSibling) {
            console.warn('Expected copy-paste icon is missing from the DOM structure');
            return;
        }

        const paramName = element.parentElement.nextElementSibling
            .textContent.trim().split(' ')[0];
        const fullParamName = paramPrefix ? `${paramPrefix}${paramName}` : paramName;

        element.setAttribute('title', fullParamName);
    });

    /**
     * Copy the list of feature names formatted as a Python list.
     *
     * @param {HTMLElement} element - The copy button inside a `.features` block; its siblings
     *   contain a `details` element and a table containing feature named.
     * @returns {boolean} Always returns `false` so callers can prevent the default click behavior.
     */
    function copyFeatureNamesToClipboard(element) {
        var detailsElem = element.closest('.features').querySelector('details');
        var wasOpen = detailsElem.open;
        detailsElem.open = true;
        var content = element.closest('.features').querySelector('tbody')
                      .innerText.trim();
        if (!wasOpen) detailsElem.open = false;
        const rows = content.split('\n').map(row => `    "${row}"`);
        const formattedText = `[\n${rows.join(',\n')},\n]`;
        const originalHTML = element.innerHTML.replace('✔', '');
        const originalStyle = element.style;
        const copyMark = document.createElement('span');
        copyMark.innerHTML = '✔';
        copyMark.style.color = 'blue';
        copyMark.style.fontSize = '1em';

        navigator.clipboard.writeText(formattedText)
            .then(() => {
                element.style.display = 'none';
                element.parentElement.appendChild(copyMark);

                setTimeout(() => {
                    copyMark.remove();
                    element.innerHTML = originalHTML;
                    element.style = originalStyle;
                }, 1000);
            })
            .catch(err => {
                console.error('Failed to copy:', err);
                element.style.color = 'orange';
                element.innerHTML = "Failed!";
                setTimeout(() => {
                    element.innerHTML = originalHTML;
                    element.style = originalStyle;
                }, 1000);
            });
        return false;
    }
    /**
     * Adapted from Skrub
     * https://github.com/skrub-data/skrub/blob/403466d1d5d4dc76a7ef569b3f8228db59a31dc3/skrub/_reporting/_data/templates/report.js#L789
     * @returns "light" or "dark"
     */
    function detectTheme(element) {
        const body = document.querySelector('body');

        // Check VSCode theme
        const themeKindAttr = body.getAttribute('data-vscode-theme-kind');
        const themeNameAttr = body.getAttribute('data-vscode-theme-name');

        if (themeKindAttr && themeNameAttr) {
            const themeKind = themeKindAttr.toLowerCase();
            const themeName = themeNameAttr.toLowerCase();

            if (themeKind.includes("dark") || themeName.includes("dark")) {
                return "dark";
            }
            if (themeKind.includes("light") || themeName.includes("light")) {
                return "light";
            }
        }

        // Check Jupyter theme
        if (body.getAttribute('data-jp-theme-light') === 'false') {
            return 'dark';
        } else if (body.getAttribute('data-jp-theme-light') === 'true') {
            return 'light';
        }

        // Guess based on a parent element's color
        const color = window.getComputedStyle(element.parentNode, null).getPropertyValue('color');
        const match = color.match(/^rgb\s*\(\s*(\d+)\s*,\s*(\d+)\s*,\s*(\d+)\s*\)\s*$/i);
        if (match) {
            const [r, g, b] = [
                parseFloat(match[1]),
                parseFloat(match[2]),
                parseFloat(match[3])
            ];

            // https://en.wikipedia.org/wiki/HSL_and_HSV#Lightness
            const luma = 0.299 * r + 0.587 * g + 0.114 * b;

            if (luma > 180) {
                // If the text is very bright we have a dark theme
                return 'dark';
            }
            if (luma < 75) {
                // If the text is very dark we have a light theme
                return 'light';
            }
            // Otherwise fall back to the next heuristic.
        }

        // Fallback to system preference
        return window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light';
    }


    function forceTheme(elementId) {
        const estimatorElement = document.querySelector(`#${elementId}`);
        if (estimatorElement === null) {
            console.error(`Element with id ${elementId} not found.`);
        } else {
            const theme = detectTheme(estimatorElement);
            estimatorElement.classList.add(theme);
        }
    }

    forceTheme('sk-container-id-25');</script></body>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 49-57

Plotting partial dependence for two features
============================================

We plot partial dependence curves for features "age" and "bmi" (body mass
index) for the decision tree. With two features,
:func:`~sklearn.inspection.PartialDependenceDisplay.from_estimator` expects to plot
two curves. Here the plot function place a grid of two plots using the space
defined by `ax` .

.. GENERATED FROM PYTHON SOURCE LINES 57-61

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(12, 6))
    ax.set_title("Decision Tree")
    tree_disp = PartialDependenceDisplay.from_estimator(tree, X, ["age", "bmi"], ax=ax)




.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_001.png
   :alt: Decision Tree
   :srcset: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 62-66

The partial dependence curves can be plotted for the multi-layer perceptron.
In this case, `line_kw` is passed to
:func:`~sklearn.inspection.PartialDependenceDisplay.from_estimator` to change the
color of the curve.

.. GENERATED FROM PYTHON SOURCE LINES 66-72

.. code-block:: Python

    fig, ax = plt.subplots(figsize=(12, 6))
    ax.set_title("Multi-layer Perceptron")
    mlp_disp = PartialDependenceDisplay.from_estimator(
        mlp, X, ["age", "bmi"], ax=ax, line_kw={"color": "red"}
    )




.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_002.png
   :alt: Multi-layer Perceptron
   :srcset: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 73-90

Plotting partial dependence of the two models together
======================================================

The `tree_disp` and `mlp_disp`
:class:`~sklearn.inspection.PartialDependenceDisplay` objects contain all the
computed information needed to recreate the partial dependence curves. This
means we can easily create additional plots without needing to recompute the
curves.

One way to plot the curves is to place them in the same figure, with the
curves of each model on each row. First, we create a figure with two axes
within two rows and one column. The two axes are passed to the
:func:`~sklearn.inspection.PartialDependenceDisplay.plot` functions of
`tree_disp` and `mlp_disp`. The given axes will be used by the plotting
function to draw the partial dependence. The resulting plot places the
decision tree partial dependence curves in the first row of the
multi-layer perceptron in the second row.

.. GENERATED FROM PYTHON SOURCE LINES 90-97

.. code-block:: Python


    fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(10, 10))
    tree_disp.plot(ax=ax1)
    ax1.set_title("Decision Tree")
    mlp_disp.plot(ax=ax2, line_kw={"color": "red"})
    ax2.set_title("Multi-layer Perceptron")




.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_003.png
   :alt: Decision Tree, Multi-layer Perceptron
   :srcset: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Multi-layer Perceptron')



.. GENERATED FROM PYTHON SOURCE LINES 98-103

Another way to compare the curves is to plot them on top of each other. Here,
we create a figure with one row and two columns. The axes are passed into the
:func:`~sklearn.inspection.PartialDependenceDisplay.plot` function as a list,
which will plot the partial dependence curves of each model on the same axes.
The length of the axes list must be equal to the number of plots drawn.

.. GENERATED FROM PYTHON SOURCE LINES 103-112

.. code-block:: Python


    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 6))
    tree_disp.plot(ax=[ax1, ax2], line_kw={"label": "Decision Tree"})
    mlp_disp.plot(
        ax=[ax1, ax2], line_kw={"label": "Multi-layer Perceptron", "color": "red"}
    )
    ax1.legend()
    ax2.legend()




.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_004.png
   :alt: plot partial dependence visualization api
   :srcset: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_004.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <matplotlib.legend.Legend object at 0x718b481252b0>



.. GENERATED FROM PYTHON SOURCE LINES 114-120

`tree_disp.axes_` is a numpy array container the axes used to draw the
partial dependence plots. This can be passed to `mlp_disp` to have the same
affect of drawing the plots on top of each other. Furthermore, the
`mlp_disp.figure_` stores the figure, which allows for resizing the figure
after calling `plot`. In this case `tree_disp.axes_` has two dimensions, thus
`plot` will only show the y label and y ticks on the left most plot.

.. GENERATED FROM PYTHON SOURCE LINES 120-130

.. code-block:: Python


    tree_disp.plot(line_kw={"label": "Decision Tree"})
    mlp_disp.plot(
        line_kw={"label": "Multi-layer Perceptron", "color": "red"}, ax=tree_disp.axes_
    )
    tree_disp.figure_.set_size_inches(10, 6)
    tree_disp.axes_[0, 0].legend()
    tree_disp.axes_[0, 1].legend()
    plt.show()




.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_005.png
   :alt: plot partial dependence visualization api
   :srcset: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_005.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 131-137

Plotting partial dependence for one feature
===========================================

Here, we plot the partial dependence curves for a single feature, "age", on
the same axes. In this case, `tree_disp.axes_` is passed into the second
plot function.

.. GENERATED FROM PYTHON SOURCE LINES 137-141

.. code-block:: Python

    tree_disp = PartialDependenceDisplay.from_estimator(tree, X, ["age"])
    mlp_disp = PartialDependenceDisplay.from_estimator(
        mlp, X, ["age"], ax=tree_disp.axes_, line_kw={"color": "red"}
    )



.. image-sg:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_006.png
   :alt: plot partial dependence visualization api
   :srcset: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_visualization_api_006.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 9.063 seconds)


.. _sphx_glr_download_auto_examples_inspection_plot_partial_dependence_visualization_api.py:

.. only:: html

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

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

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

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

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

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

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


.. include:: plot_partial_dependence_visualization_api.recommendations


.. only:: html

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

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