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

    Click :ref:`here <sphx_glr_download_auto_examples_compose_plot_transformed_target.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_compose_plot_transformed_target.py:


======================================================
Effect of transforming the targets in regression model
======================================================

In this example, we give an overview of the
:class:`sklearn.compose.TransformedTargetRegressor`. Two examples
illustrate the benefit of transforming the targets before learning a linear
regression model. The first example uses synthetic data while the second
example is based on the Boston housing data set.




.. code-block:: python


    # Author: Guillaume Lemaitre <guillaume.lemaitre@inria.fr>
    # License: BSD 3 clause

    from __future__ import print_function, division

    import numpy as np
    import matplotlib.pyplot as plt

    print(__doc__)


Synthetic example
##############################################################################



.. code-block:: python


    from sklearn.datasets import make_regression
    from sklearn.model_selection import train_test_split
    from sklearn.linear_model import RidgeCV
    from sklearn.compose import TransformedTargetRegressor
    from sklearn.metrics import median_absolute_error, r2_score


A synthetic random regression problem is generated. The targets ``y`` are
modified by: (i) translating all targets such that all entries are
non-negative and (ii) applying an exponential function to obtain non-linear
targets which cannot be fitted using a simple linear model.

Therefore, a logarithmic (`np.log1p`) and an exponential function
(`np.expm1`) will be used to transform the targets before training a linear
regression model and using it for prediction.



.. code-block:: python


    X, y = make_regression(n_samples=10000, noise=100, random_state=0)
    y = np.exp((y + abs(y.min())) / 200)
    y_trans = np.log1p(y)


The following illustrate the probability density functions of the target
before and after applying the logarithmic functions.



.. code-block:: python


    f, (ax0, ax1) = plt.subplots(1, 2)

    ax0.hist(y, bins=100, normed=True)
    ax0.set_xlim([0, 2000])
    ax0.set_ylabel('Probability')
    ax0.set_xlabel('Target')
    ax0.set_title('Target distribution')

    ax1.hist(y_trans, bins=100, normed=True)
    ax1.set_ylabel('Probability')
    ax1.set_xlabel('Target')
    ax1.set_title('Transformed target distribution')

    f.suptitle("Synthetic data", y=0.035)
    f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])

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


At first, a linear model will be applied on the original targets. Due to the
non-linearity, the model trained will not be precise during the
prediction. Subsequently, a logarithmic function is used to linearize the
targets, allowing better prediction even with a similar linear model as
reported by the median absolute error (MAE).



.. code-block:: python


    f, (ax0, ax1) = plt.subplots(1, 2, sharey=True)

    regr = RidgeCV()
    regr.fit(X_train, y_train)
    y_pred = regr.predict(X_test)

    ax0.scatter(y_test, y_pred)
    ax0.plot([0, 2000], [0, 2000], '--k')
    ax0.set_ylabel('Target predicted')
    ax0.set_xlabel('True Target')
    ax0.set_title('Ridge regression \n without target transformation')
    ax0.text(100, 1750, r'$R^2$=%.2f, MAE=%.2f' % (
        r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
    ax0.set_xlim([0, 2000])
    ax0.set_ylim([0, 2000])

    regr_trans = TransformedTargetRegressor(regressor=RidgeCV(),
                                            func=np.log1p,
                                            inverse_func=np.expm1)
    regr_trans.fit(X_train, y_train)
    y_pred = regr_trans.predict(X_test)

    ax1.scatter(y_test, y_pred)
    ax1.plot([0, 2000], [0, 2000], '--k')
    ax1.set_ylabel('Target predicted')
    ax1.set_xlabel('True Target')
    ax1.set_title('Ridge regression \n with target transformation')
    ax1.text(100, 1750, r'$R^2$=%.2f, MAE=%.2f' % (
        r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
    ax1.set_xlim([0, 2000])
    ax1.set_ylim([0, 2000])

    f.suptitle("Synthetic data", y=0.035)
    f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])


Real-world data set
##############################################################################


In a similar manner, the boston housing data set is used to show the impact
of transforming the targets before learning a model. In this example, the
targets to be predicted corresponds to the weighted distances to the five
Boston employment centers.



.. code-block:: python


    from sklearn.datasets import load_boston
    from sklearn.preprocessing import QuantileTransformer, quantile_transform

    dataset = load_boston()
    target = np.array(dataset.feature_names) == "DIS"
    X = dataset.data[:, np.logical_not(target)]
    y = dataset.data[:, target].squeeze()
    y_trans = quantile_transform(dataset.data[:, target],
                                 output_distribution='normal').squeeze()


A :class:`sklearn.preprocessing.QuantileTransformer` is used such that the
targets follows a normal distribution before applying a
:class:`sklearn.linear_model.RidgeCV` model.



.. code-block:: python


    f, (ax0, ax1) = plt.subplots(1, 2)

    ax0.hist(y, bins=100, normed=True)
    ax0.set_ylabel('Probability')
    ax0.set_xlabel('Target')
    ax0.set_title('Target distribution')

    ax1.hist(y_trans, bins=100, normed=True)
    ax1.set_ylabel('Probability')
    ax1.set_xlabel('Target')
    ax1.set_title('Transformed target distribution')

    f.suptitle("Boston housing data: distance to employment centers", y=0.035)
    f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])

    X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)


The effect of the transformer is weaker than on the synthetic data. However,
the transform induces a decrease of the MAE.



.. code-block:: python


    f, (ax0, ax1) = plt.subplots(1, 2, sharey=True)

    regr = RidgeCV()
    regr.fit(X_train, y_train)
    y_pred = regr.predict(X_test)

    ax0.scatter(y_test, y_pred)
    ax0.plot([0, 10], [0, 10], '--k')
    ax0.set_ylabel('Target predicted')
    ax0.set_xlabel('True Target')
    ax0.set_title('Ridge regression \n without target transformation')
    ax0.text(1, 9, r'$R^2$=%.2f, MAE=%.2f' % (
        r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
    ax0.set_xlim([0, 10])
    ax0.set_ylim([0, 10])

    regr_trans = TransformedTargetRegressor(
        regressor=RidgeCV(),
        transformer=QuantileTransformer(output_distribution='normal'))
    regr_trans.fit(X_train, y_train)
    y_pred = regr_trans.predict(X_test)

    ax1.scatter(y_test, y_pred)
    ax1.plot([0, 10], [0, 10], '--k')
    ax1.set_ylabel('Target predicted')
    ax1.set_xlabel('True Target')
    ax1.set_title('Ridge regression \n with target transformation')
    ax1.text(1, 9, r'$R^2$=%.2f, MAE=%.2f' % (
        r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)))
    ax1.set_xlim([0, 10])
    ax1.set_ylim([0, 10])

    f.suptitle("Boston housing data: distance to employment centers", y=0.035)
    f.tight_layout(rect=[0.05, 0.05, 0.95, 0.95])

    plt.show()

**Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_compose_plot_transformed_target.py:


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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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