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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/compose/plot_transformed_target.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. 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
:class:`~sklearn.compose.TransformedTargetRegressor`. We use two examples
to 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 Ames housing data set.

.. GENERATED FROM PYTHON SOURCE LINES 14-27

.. code-block:: default


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

    import numpy as np
    import matplotlib.pyplot as plt

    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








.. GENERATED FROM PYTHON SOURCE LINES 28-30

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

.. GENERATED FROM PYTHON SOURCE LINES 32-43

A synthetic random regression dataset is generated. The targets ``y`` are
modified by:

  1. translating all targets such that all entries are
     non-negative (by adding the absolute value of the lowest ``y``) and
  2. 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.

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: default


    X, y = make_regression(n_samples=10000, noise=100, random_state=0)
    y = np.expm1((y + abs(y.min())) / 200)
    y_trans = np.log1p(y)








.. GENERATED FROM PYTHON SOURCE LINES 49-51

Below we plot the probability density functions of the target
before and after applying the logarithmic functions.

.. GENERATED FROM PYTHON SOURCE LINES 51-70

.. code-block:: default


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

    ax0.hist(y, bins=100, density=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, density=True)
    ax1.set_ylabel("Probability")
    ax1.set_xlabel("Target")
    ax1.set_title("Transformed target distribution")

    f.suptitle("Synthetic data", y=0.06, x=0.53)
    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)




.. image-sg:: /auto_examples/compose/images/sphx_glr_plot_transformed_target_001.png
   :alt: Synthetic data, Target distribution, Transformed target distribution
   :srcset: /auto_examples/compose/images/sphx_glr_plot_transformed_target_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 71-76

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
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).

.. GENERATED FROM PYTHON SOURCE LINES 76-120

.. code-block:: default


    f, (ax0, ax1) = plt.subplots(1, 2, sharey=True)
    # Use linear model
    regr = RidgeCV()
    regr.fit(X_train, y_train)
    y_pred = regr.predict(X_test)
    # Plot results
    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])
    # Transform targets and use same linear model
    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])




.. image-sg:: /auto_examples/compose/images/sphx_glr_plot_transformed_target_002.png
   :alt: Synthetic data, Ridge regression   without target transformation, Ridge regression   with target transformation
   :srcset: /auto_examples/compose/images/sphx_glr_plot_transformed_target_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 121-127

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

 In a similar manner, the Ames housing data set is used to show the impact
 of transforming the targets before learning a model. In this example, the
 target to be predicted is the selling price of each house.

.. GENERATED FROM PYTHON SOURCE LINES 127-140

.. code-block:: default


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

    ames = fetch_openml(name="house_prices", as_frame=True)
    # Keep only numeric columns
    X = ames.data.select_dtypes(np.number)
    # Remove columns with NaN or Inf values
    X = X.drop(columns=["LotFrontage", "GarageYrBlt", "MasVnrArea"])
    y = ames.target
    y_trans = quantile_transform(
        y.to_frame(), n_quantiles=900, output_distribution="normal", copy=True
    ).squeeze()


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

.. code-block:: pytb

    Traceback (most recent call last):
      File "/build/scikit-learn-GiwEwR/scikit-learn-1.1.2+dfsg/examples/compose/plot_transformed_target.py", line 131, in <module>
        ames = fetch_openml(name="house_prices", as_frame=True)
               ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      File "/build/scikit-learn-GiwEwR/scikit-learn-1.1.2+dfsg/.pybuild/cpython3_3.11/build/sklearn/datasets/_openml.py", line 726, in fetch_openml
        raise TimeoutError('Debian Policy Section 4.9 prohibits network access during build')
    TimeoutError: Debian Policy Section 4.9 prohibits network access during build




.. GENERATED FROM PYTHON SOURCE LINES 141-144

A :class:`~sklearn.preprocessing.QuantileTransformer` is used to normalize
the target distribution before applying a
:class:`~sklearn.linear_model.RidgeCV` model.

.. GENERATED FROM PYTHON SOURCE LINES 144-163

.. code-block:: default


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

    ax0.hist(y, bins=100, density=True)
    ax0.set_ylabel("Probability")
    ax0.set_xlabel("Target")
    ax0.text(s="Target distribution", x=1.2e5, y=9.8e-6, fontsize=12)
    ax0.ticklabel_format(axis="both", style="sci", scilimits=(0, 0))

    ax1.hist(y_trans, bins=100, density=True)
    ax1.set_ylabel("Probability")
    ax1.set_xlabel("Target")
    ax1.text(s="Transformed target distribution", x=-6.8, y=0.479, fontsize=12)

    f.suptitle("Ames housing data: selling price", y=0.04)
    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)


.. GENERATED FROM PYTHON SOURCE LINES 164-171

The effect of the transformer is weaker than on the synthetic data. However,
the transformation results in an increase in :math:`R^2` and large decrease
of the MAE. The residual plot (predicted target - true target vs predicted
target) without target transformation takes on a curved, 'reverse smile'
shape due to residual values that vary depending on the value of predicted
target. With target transformation, the shape is more linear indicating
better model fit.

.. GENERATED FROM PYTHON SOURCE LINES 171-240

.. code-block:: default


    f, (ax0, ax1) = plt.subplots(2, 2, sharey="row", figsize=(6.5, 8))

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

    ax0[0].scatter(y_pred, y_test, s=8)
    ax0[0].plot([0, 7e5], [0, 7e5], "--k")
    ax0[0].set_ylabel("True target")
    ax0[0].set_xlabel("Predicted target")
    ax0[0].text(
        s="Ridge regression \n without target transformation",
        x=-5e4,
        y=8e5,
        fontsize=12,
        multialignment="center",
    )
    ax0[0].text(
        3e4,
        64e4,
        r"$R^2$=%.2f, MAE=%.2f"
        % (r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)),
    )
    ax0[0].set_xlim([0, 7e5])
    ax0[0].set_ylim([0, 7e5])
    ax0[0].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))

    ax1[0].scatter(y_pred, (y_pred - y_test), s=8)
    ax1[0].set_ylabel("Residual")
    ax1[0].set_xlabel("Predicted target")
    ax1[0].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))

    regr_trans = TransformedTargetRegressor(
        regressor=RidgeCV(),
        transformer=QuantileTransformer(n_quantiles=900, output_distribution="normal"),
    )
    regr_trans.fit(X_train, y_train)
    y_pred = regr_trans.predict(X_test)

    ax0[1].scatter(y_pred, y_test, s=8)
    ax0[1].plot([0, 7e5], [0, 7e5], "--k")
    ax0[1].set_ylabel("True target")
    ax0[1].set_xlabel("Predicted target")
    ax0[1].text(
        s="Ridge regression \n with target transformation",
        x=-5e4,
        y=8e5,
        fontsize=12,
        multialignment="center",
    )
    ax0[1].text(
        3e4,
        64e4,
        r"$R^2$=%.2f, MAE=%.2f"
        % (r2_score(y_test, y_pred), median_absolute_error(y_test, y_pred)),
    )
    ax0[1].set_xlim([0, 7e5])
    ax0[1].set_ylim([0, 7e5])
    ax0[1].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))

    ax1[1].scatter(y_pred, (y_pred - y_test), s=8)
    ax1[1].set_ylabel("Residual")
    ax1[1].set_xlabel("Predicted target")
    ax1[1].ticklabel_format(axis="both", style="sci", scilimits=(0, 0))

    f.suptitle("Ames housing data: selling price", y=0.035)

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.574 seconds)


.. _sphx_glr_download_auto_examples_compose_plot_transformed_target.py:


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



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