.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/ensemble/plot_monotonic_constraints.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_ensemble_plot_monotonic_constraints.py>`
        to download the full example code. or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_ensemble_plot_monotonic_constraints.py:


=====================
单调约束
=====================

这个例子说明了单调约束对梯度提升估计器的影响。

我们构建了一个人工数据集，其中目标值通常与第一个特征正相关（带有一些随机和非随机的变化），
并且通常与第二个特征负相关。

通过在学习过程中分别对特征施加单调增加或单调减少的约束，估计器能够正确地遵循总体趋势，
而不是受到变化的影响。

这个例子灵感来自于 `XGBoost 文档
<https://xgboost.readthedocs.io/en/latest/tutorials/monotonic.html>`_  。

.. GENERATED FROM PYTHON SOURCE LINES 20-38

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.ensemble import HistGradientBoostingRegressor
    from sklearn.inspection import PartialDependenceDisplay

    rng = np.random.RandomState(0)

    n_samples = 1000
    f_0 = rng.rand(n_samples)
    f_1 = rng.rand(n_samples)
    X = np.c_[f_0, f_1]
    noise = rng.normal(loc=0.0, scale=0.01, size=n_samples)

    # y 与 f_0 正相关，与 f_1 负相关
    y = 5 * f_0 + np.sin(10 * np.pi * f_0) - 5 * f_1 - np.cos(10 * np.pi * f_1) + noise









.. GENERATED FROM PYTHON SOURCE LINES 39-40

在此数据集上拟合第一个没有任何约束的模型。

.. GENERATED FROM PYTHON SOURCE LINES 40-44

.. code-block:: Python


    gbdt_no_cst = HistGradientBoostingRegressor()
    gbdt_no_cst.fit(X, y)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>#sk-container-id-23 {
      /* Definition of color scheme common for light and dark mode */
      --sklearn-color-text: black;
      --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;

      /* Specific color for light theme */
      --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));
      --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));
      --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));
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      margin: 0 0.4em 0.5em 0.4em;
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    #sk-container-id-23 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;
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    #sk-container-id-23 div.sk-text-repr-fallback {
      display: none;
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    div.sk-parallel-item,
    div.sk-serial,
    div.sk-item {
      /* draw centered vertical line to link estimators */
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      background-repeat: no-repeat;
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    /* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is
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    - Pipeline and ColumnTransformer use this feature and define the default style
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    */

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    .sk-estimator-doc-link,
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      /* fitted */
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      color: var(--sklearn-color-background);
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      width: 1rem;
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    }
    </style><div id="sk-container-id-23" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>HistGradientBoostingRegressor()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-99" type="checkbox" checked><label for="sk-estimator-id-99" class="sk-toggleable__label fitted sk-toggleable__label-arrow fitted">&nbsp;&nbsp;HistGradientBoostingRegressor<a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/dev/modules/generated/sklearn.ensemble.HistGradientBoostingRegressor.html">?<span>Documentation for HistGradientBoostingRegressor</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></label><div class="sk-toggleable__content fitted"><pre>HistGradientBoostingRegressor()</pre></div> </div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 45-46

在此数据集上分别拟合一个具有单调增加（1）和单调减少（-1）约束的第二模型。

.. GENERATED FROM PYTHON SOURCE LINES 46-51

.. code-block:: Python


    gbdt_with_monotonic_cst = HistGradientBoostingRegressor(monotonic_cst=[1, -1])
    gbdt_with_monotonic_cst.fit(X, y)







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <style>#sk-container-id-24 {
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      /* Definition of color scheme for unfitted estimators */
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    - Pipeline and ColumnTransformer use this feature and define the default style
    - Estimators will overwrite some part of the style using the `sk-estimator` class
    */

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    /* Toggleable content - dropdown */

    #sk-container-id-24 div.sk-toggleable__content {
      max-height: 0;
      max-width: 0;
      overflow: hidden;
      text-align: left;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-24 div.sk-toggleable__content.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-24 div.sk-toggleable__content pre {
      margin: 0.2em;
      border-radius: 0.25em;
      color: var(--sklearn-color-text);
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-24 div.sk-toggleable__content.fitted pre {
      /* unfitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    #sk-container-id-24 input.sk-toggleable__control:checked~div.sk-toggleable__content {
      /* Expand drop-down */
      max-height: 200px;
      max-width: 100%;
      overflow: auto;
    }

    #sk-container-id-24 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {
      content: "â–¾";
    }

    /* Pipeline/ColumnTransformer-specific style */

    #sk-container-id-24 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-24 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator-specific style */

    /* Colorize estimator box */
    #sk-container-id-24 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-24 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

    #sk-container-id-24 div.sk-label label.sk-toggleable__label,
    #sk-container-id-24 div.sk-label label {
      /* The background is the default theme color */
      color: var(--sklearn-color-text-on-default-background);
    }

    /* On hover, darken the color of the background */
    #sk-container-id-24 div.sk-label:hover label.sk-toggleable__label {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    /* Label box, darken color on hover, fitted */
    #sk-container-id-24 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {
      color: var(--sklearn-color-text);
      background-color: var(--sklearn-color-fitted-level-2);
    }

    /* Estimator label */

    #sk-container-id-24 div.sk-label label {
      font-family: monospace;
      font-weight: bold;
      display: inline-block;
      line-height: 1.2em;
    }

    #sk-container-id-24 div.sk-label-container {
      text-align: center;
    }

    /* Estimator-specific */
    #sk-container-id-24 div.sk-estimator {
      font-family: monospace;
      border: 1px dotted var(--sklearn-color-border-box);
      border-radius: 0.25em;
      box-sizing: border-box;
      margin-bottom: 0.5em;
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-0);
    }

    #sk-container-id-24 div.sk-estimator.fitted {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-0);
    }

    /* on hover */
    #sk-container-id-24 div.sk-estimator:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-2);
    }

    #sk-container-id-24 div.sk-estimator.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-2);
    }

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

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

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

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

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

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

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

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

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

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

    #sk-container-id-24 a.estimator_doc_link {
      float: right;
      font-size: 1rem;
      line-height: 1em;
      font-family: monospace;
      background-color: var(--sklearn-color-background);
      border-radius: 1rem;
      height: 1rem;
      width: 1rem;
      text-decoration: none;
      /* unfitted */
      color: var(--sklearn-color-unfitted-level-1);
      border: var(--sklearn-color-unfitted-level-1) 1pt solid;
    }

    #sk-container-id-24 a.estimator_doc_link.fitted {
      /* fitted */
      border: var(--sklearn-color-fitted-level-1) 1pt solid;
      color: var(--sklearn-color-fitted-level-1);
    }

    /* On hover */
    #sk-container-id-24 a.estimator_doc_link:hover {
      /* unfitted */
      background-color: var(--sklearn-color-unfitted-level-3);
      color: var(--sklearn-color-background);
      text-decoration: none;
    }

    #sk-container-id-24 a.estimator_doc_link.fitted:hover {
      /* fitted */
      background-color: var(--sklearn-color-fitted-level-3);
    }
    </style><div id="sk-container-id-24" class="sk-top-container"><div class="sk-text-repr-fallback"><pre>HistGradientBoostingRegressor(monotonic_cst=[1, -1])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class="sk-container" hidden><div class="sk-item"><div class="sk-estimator fitted sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-100" type="checkbox" checked><label for="sk-estimator-id-100" class="sk-toggleable__label fitted sk-toggleable__label-arrow fitted">&nbsp;&nbsp;HistGradientBoostingRegressor<a class="sk-estimator-doc-link fitted" rel="noreferrer" target="_blank" href="https://scikit-learn.org/dev/modules/generated/sklearn.ensemble.HistGradientBoostingRegressor.html">?<span>Documentation for HistGradientBoostingRegressor</span></a><span class="sk-estimator-doc-link fitted">i<span>Fitted</span></span></label><div class="sk-toggleable__content fitted"><pre>HistGradientBoostingRegressor(monotonic_cst=[1, -1])</pre></div> </div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 52-53

让我们展示预测结果对这两个特征的部分依赖性。

.. GENERATED FROM PYTHON SOURCE LINES 53-84

.. code-block:: Python


    fig, ax = plt.subplots()
    disp = PartialDependenceDisplay.from_estimator(
        gbdt_no_cst,
        X,
        features=[0, 1],
        feature_names=(
            "First feature",
            "Second feature",
        ),
        line_kw={"linewidth": 4, "label": "unconstrained", "color": "tab:blue"},
        ax=ax,
    )
    PartialDependenceDisplay.from_estimator(
        gbdt_with_monotonic_cst,
        X,
        features=[0, 1],
        line_kw={"linewidth": 4, "label": "constrained", "color": "tab:orange"},
        ax=disp.axes_,
    )

    for f_idx in (0, 1):
        disp.axes_[0, f_idx].plot(
            X[:, f_idx], y, "o", alpha=0.3, zorder=-1, color="tab:green"
        )
        disp.axes_[0, f_idx].set_ylim(-6, 6)

    plt.legend()
    fig.suptitle("Monotonic constraints effect on partial dependences")
    plt.show()




.. image-sg:: /auto_examples/ensemble/images/sphx_glr_plot_monotonic_constraints_001.png
   :alt: Monotonic constraints effect on partial dependences
   :srcset: /auto_examples/ensemble/images/sphx_glr_plot_monotonic_constraints_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 85-86

我们可以看到，无约束模型的预测捕捉到了数据的波动，而约束模型则遵循总体趋势，忽略了局部变化。

.. GENERATED FROM PYTHON SOURCE LINES 89-94

.. _monotonic_cst_features_names:

使用特征名称指定单调约束

请注意，如果训练数据具有特征名称，可以通过传递字典来指定单调约束：

.. GENERATED FROM PYTHON SOURCE LINES 94-105

.. code-block:: Python

    import pandas as pd

    X_df = pd.DataFrame(X, columns=["f_0", "f_1"])

    gbdt_with_monotonic_cst_df = HistGradientBoostingRegressor(
        monotonic_cst={"f_0": 1, "f_1": -1}
    ).fit(X_df, y)

    np.allclose(
        gbdt_with_monotonic_cst_df.predict(X_df), gbdt_with_monotonic_cst.predict(X)
    )




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

 .. code-block:: none


    True




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

   **Total running time of the script:** (0 minutes 0.562 seconds)


.. _sphx_glr_download_auto_examples_ensemble_plot_monotonic_constraints.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/ensemble/plot_monotonic_constraints.ipynb
        :alt: Launch binder
        :width: 150 px

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

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

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

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

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

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


.. include:: plot_monotonic_constraints.recommendations


.. only:: html

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

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