
.. 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:


=====================
Monotonic Constraints
=====================

This example illustrates the effect of monotonic constraints on a gradient
boosting estimator.

We build an artificial dataset where the target value is in general
positively correlated with the first feature (with some random and
non-random variations), and in general negatively correlated with the second
feature.

By imposing a monotonic increase or a monotonic decrease constraint, respectively,
on the features during the learning process, the estimator is able to properly follow
the general trend instead of being subject to the variations.

This example was inspired by the `XGBoost documentation
<https://xgboost.readthedocs.io/en/latest/tutorials/monotonic.html>`_.

.. GENERATED FROM PYTHON SOURCE LINES 23-41

.. code-block:: default

    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 is positively correlated with f_0, and negatively correlated with f_1
    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 42-43

Fit a first model on this dataset without any constraints.

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: default

    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-22 {color: black;}#sk-container-id-22 pre{padding: 0;}#sk-container-id-22 div.sk-toggleable {background-color: white;}#sk-container-id-22 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-22 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-22 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-22 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-22 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-22 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-22 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-22 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-22 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-22 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-22 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-22 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-22 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-22 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-22 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-22 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-22 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-22 div.sk-item {position: relative;z-index: 1;}#sk-container-id-22 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-22 div.sk-item::before, #sk-container-id-22 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-22 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-22 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-22 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-22 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-22 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-22 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-22 div.sk-label-container {text-align: center;}#sk-container-id-22 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-container-id-22 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-22" 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 sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-102" type="checkbox" checked><label for="sk-estimator-id-102" class="sk-toggleable__label sk-toggleable__label-arrow">HistGradientBoostingRegressor</label><div class="sk-toggleable__content"><pre>HistGradientBoostingRegressor()</pre></div></div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 47-49

Fit a second model on this dataset with monotonic increase (1)
and a monotonic decrease (-1) constraints, respectively.

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: default

    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-23 {color: black;}#sk-container-id-23 pre{padding: 0;}#sk-container-id-23 div.sk-toggleable {background-color: white;}#sk-container-id-23 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-23 label.sk-toggleable__label-arrow:before {content: "▸";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-23 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-23 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-23 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-23 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-23 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-23 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: "▾";}#sk-container-id-23 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-23 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-23 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-23 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-23 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-23 div.sk-parallel-item::after {content: "";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-23 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-23 div.sk-serial::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-23 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-23 div.sk-item {position: relative;z-index: 1;}#sk-container-id-23 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-23 div.sk-item::before, #sk-container-id-23 div.sk-parallel-item::before {content: "";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-23 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-23 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-23 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-23 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-23 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-23 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-23 div.sk-label-container {text-align: center;}#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;}#sk-container-id-23 div.sk-text-repr-fallback {display: none;}</style><div id="sk-container-id-23" 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 sk-toggleable"><input class="sk-toggleable__control sk-hidden--visually" id="sk-estimator-id-103" type="checkbox" checked><label for="sk-estimator-id-103" class="sk-toggleable__label sk-toggleable__label-arrow">HistGradientBoostingRegressor</label><div class="sk-toggleable__content"><pre>HistGradientBoostingRegressor(monotonic_cst=[1, -1])</pre></div></div></div></div></div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 54-55

Let's display the partial dependence of the predictions on the two features.

.. GENERATED FROM PYTHON SOURCE LINES 55-85

.. code-block:: default

    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 86-89

We can see that the predictions of the unconstrained model capture the
oscillations of the data while the constrained model follows the general
trend and ignores the local variations.

.. GENERATED FROM PYTHON SOURCE LINES 91-98

.. _monotonic_cst_features_names:

Using feature names to specify monotonic constraints
----------------------------------------------------

Note that if the training data has feature names, it's possible to specify the
monotonic constraints by passing a dictionary:

.. GENERATED FROM PYTHON SOURCE LINES 98-109

.. code-block:: default

    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 0.516 seconds)


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