.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_inspection_plot_partial_dependence.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_inspection_plot_partial_dependence.py:


========================
Partial Dependence Plots
========================

Partial dependence plots show the dependence between the target function [2]_
and a set of 'target' features, marginalizing over the values of all other
features (the complement features). Due to the limits of human perception, the
size of the target feature set must be small (usually, one or two) thus the
target features are usually chosen among the most important features.

This example shows how to obtain partial dependence plots from a
:class:`~sklearn.neural_network.MLPRegressor` and a
:class:`~sklearn.ensemble.HistGradientBoostingRegressor` trained on the
California housing dataset. The example is taken from [1]_.

The plots show four 1-way and two 1-way partial dependence plots (omitted for
:class:`~sklearn.neural_network.MLPRegressor` due to computation time). The
target variables for the one-way PDP are: median income (`MedInc`), average
occupants per household (`AvgOccup`), median house age (`HouseAge`), and
average rooms per household (`AveRooms`).

.. [1] T. Hastie, R. Tibshirani and J. Friedman, "Elements of Statistical
       Learning Ed. 2", Springer, 2009.

.. [2] For classification you can think of it as the regression score before
       the link function.


.. code-block:: default

    print(__doc__)

    from time import time
    import numpy as np
    import pandas as pd
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D

    from sklearn.model_selection import train_test_split
    from sklearn.preprocessing import QuantileTransformer
    from sklearn.pipeline import make_pipeline

    from sklearn.inspection import partial_dependence
    from sklearn.inspection import plot_partial_dependence
    from sklearn.experimental import enable_hist_gradient_boosting  # noqa
    from sklearn.ensemble import HistGradientBoostingRegressor
    from sklearn.neural_network import MLPRegressor
    from sklearn.datasets import fetch_california_housing









California Housing data preprocessing
-------------------------------------

Center target to avoid gradient boosting init bias: gradient boosting
with the 'recursion' method does not account for the initial estimator
(here the average target, by default)


.. code-block:: default


    cal_housing = fetch_california_housing()
    X = pd.DataFrame(cal_housing.data, columns=cal_housing.feature_names)
    y = cal_housing.target

    y -= y.mean()

    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1,
                                                        random_state=0)








Partial Dependence computation for multi-layer perceptron
---------------------------------------------------------

Let's fit a MLPRegressor and compute single-variable partial dependence
plots


.. code-block:: default


    print("Training MLPRegressor...")
    tic = time()
    est = make_pipeline(QuantileTransformer(),
                        MLPRegressor(hidden_layer_sizes=(50, 50),
                                     learning_rate_init=0.01,
                                     early_stopping=True))
    est.fit(X_train, y_train)
    print("done in {:.3f}s".format(time() - tic))
    print("Test R2 score: {:.2f}".format(est.score(X_test, y_test)))





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

 Out:

 .. code-block:: none

    Training MLPRegressor...
    done in 3.354s
    Test R2 score: 0.81




We configured a pipeline to scale the numerical input features and tuned the
neural network size and learning rate to get a reasonable compromise between
training time and predictive performance on a test set.

Importantly, this tabular dataset has very different dynamic ranges for its
features. Neural networks tend to be very sensitive to features with varying
scales and forgetting to preprocess the numeric feature would lead to a very
poor model.

It would be possible to get even higher predictive performance with a larger
neural network but the training would also be significantly more expensive.

Note that it is important to check that the model is accurate enough on a
test set before plotting the partial dependence since there would be little
use in explaining the impact of a given feature on the prediction function of
a poor model.

Let's now compute the partial dependence plots for this neural network using
the model-agnostic (brute-force) method:


.. code-block:: default


    print('Computing partial dependence plots...')
    tic = time()
    # We don't compute the 2-way PDP (5, 1) here, because it is a lot slower
    # with the brute method.
    features = ['MedInc', 'AveOccup', 'HouseAge', 'AveRooms']
    plot_partial_dependence(est, X_train, features,
                            n_jobs=3, grid_resolution=20)
    print("done in {:.3f}s".format(time() - tic))
    fig = plt.gcf()
    fig.suptitle('Partial dependence of house value on non-location features\n'
                 'for the California housing dataset, with MLPRegressor')
    fig.subplots_adjust(hspace=0.3)




.. image:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_001.png
    :alt: Partial dependence of house value on non-location features for the California housing dataset, with MLPRegressor
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    Computing partial dependence plots...
    done in 2.335s




Partial Dependence computation for Gradient Boosting
----------------------------------------------------

Let's now fit a GradientBoostingRegressor and compute the partial dependence
plots either or one or two variables at a time.


.. code-block:: default


    print("Training GradientBoostingRegressor...")
    tic = time()
    est = HistGradientBoostingRegressor()
    est.fit(X_train, y_train)
    print("done in {:.3f}s".format(time() - tic))
    print("Test R2 score: {:.2f}".format(est.score(X_test, y_test)))





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

 Out:

 .. code-block:: none

    Training GradientBoostingRegressor...
    done in 0.438s
    Test R2 score: 0.85




Here, we used the default hyperparameters for the gradient boosting model
without any preprocessing as tree-based models are naturally robust to
monotonic transformations of numerical features.

Note that on this tabular dataset, Gradient Boosting Machines are both
significantly faster to train and more accurate than neural networks. It is
also significantly cheaper to tune their hyperparameters (the default tend to
work well while this is not often the case for neural networks).

Finally, as we will see next, computing partial dependence plots tree-based
models is also orders of magnitude faster making it cheap to compute partial
dependence plots for pairs of interacting features:


.. code-block:: default


    print('Computing partial dependence plots...')
    tic = time()
    features = ['MedInc', 'AveOccup', 'HouseAge', 'AveRooms',
                ('AveOccup', 'HouseAge')]
    plot_partial_dependence(est, X_train, features,
                            n_jobs=3, grid_resolution=20)
    print("done in {:.3f}s".format(time() - tic))
    fig = plt.gcf()
    fig.suptitle('Partial dependence of house value on non-location features\n'
                 'for the California housing dataset, with Gradient Boosting')
    fig.subplots_adjust(wspace=0.4, hspace=0.3)





.. image:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_002.png
    :alt: Partial dependence of house value on non-location features for the California housing dataset, with Gradient Boosting
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    Computing partial dependence plots...
    done in 0.272s




Analysis of the plots
---------------------

We can clearly see that the median house price shows a linear relationship
with the median income (top left) and that the house price drops when the
average occupants per household increases (top middle).
The top right plot shows that the house age in a district does not have
a strong influence on the (median) house price; so does the average rooms
per household.
The tick marks on the x-axis represent the deciles of the feature values
in the training data.

We also observe that :class:`~sklearn.neural_network.MLPRegressor` has much
smoother predictions than
:class:`~sklearn.ensemble.HistGradientBoostingRegressor`. For the plots to be
comparable, it is necessary to subtract the average value of the target
``y``: The 'recursion' method, used by default for
:class:`~sklearn.ensemble.HistGradientBoostingRegressor`, does not account
for the initial predictor (in our case the average target). Setting the
target average to 0 avoids this bias.

Partial dependence plots with two target features enable us to visualize
interactions among them. The two-way partial dependence plot shows the
dependence of median house price on joint values of house age and average
occupants per household. We can clearly see an interaction between the
two features: for an average occupancy greater than two, the house price is
nearly independent of the house age, whereas for values less than two there
is a strong dependence on age.

3D interaction plots
--------------------

Let's make the same partial dependence plot for the 2 features interaction,
this time in 3 dimensions.


.. code-block:: default


    fig = plt.figure()

    features = ('AveOccup', 'HouseAge')
    pdp, axes = partial_dependence(est, X_train, features=features,
                                   grid_resolution=20)
    XX, YY = np.meshgrid(axes[0], axes[1])
    Z = pdp[0].T
    ax = Axes3D(fig)
    surf = ax.plot_surface(XX, YY, Z, rstride=1, cstride=1,
                           cmap=plt.cm.BuPu, edgecolor='k')
    ax.set_xlabel(features[0])
    ax.set_ylabel(features[1])
    ax.set_zlabel('Partial dependence')
    #  pretty init view
    ax.view_init(elev=22, azim=122)
    plt.colorbar(surf)
    plt.suptitle('Partial dependence of house value on median\n'
                 'age and average occupancy, with Gradient Boosting')
    plt.subplots_adjust(top=0.9)

    plt.show()



.. image:: /auto_examples/inspection/images/sphx_glr_plot_partial_dependence_003.png
    :alt: Partial dependence of house value on median age and average occupancy, with Gradient Boosting
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  6.775 seconds)


.. _sphx_glr_download_auto_examples_inspection_plot_partial_dependence.py:


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