.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/Builtin/linear_regression.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_Builtin_linear_regression.py>`
        to download the full example code.

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

.. _sphx_glr_examples_Builtin_linear_regression.py:


Linear regression
=====================
This example illustrates the use of the :class:`skwdro.linear_models.LinearRegression` class to perform a simple Wasserstein distributionally robust linear regression.

The samples are of the form :math:`\xi = (x,y) \in \mathbb{R}\times\mathbb{R}` and the sought predictor is linear.

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.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.datasets import make_regression
    from sklearn.preprocessing import minmax_scale
    from sklearn.model_selection import train_test_split
    from sklearn.metrics import mean_squared_error

    from skwdro.linear_models import LinearRegression








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Problem setup
~~~~~~~~~~~~~

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.. code-block:: Python


    n = 100 # Total number of samples
    n_train = int(np.floor(0.8 * n)) # Number of training samples
    n_test = n - n_train # Number of test samples

    # Generate some data
    X, y = make_regression(n_samples=n, n_features=1, noise=50, random_state=0)

    # Normalize the data
    X = minmax_scale(X, feature_range=(-1, 1))
    y = minmax_scale(y, feature_range=(-1, 1))

    # Split the data into training and test sets
    X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=n_train, test_size=n_test, random_state=0)








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WDRO linear regression
~~~~~~~~~~~~~~~~~~~~~~

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.. code-block:: Python


    # Define a range of radii, rho=0 corresponds to the standard linear regression
    rhos = [0., 1e-2, 1e-1]

    # Fit the model for each radius
    estimators = []
    for rho in rhos:
        print(f'Fitting model for rho={rho}')
        estimator = LinearRegression(rho=rho, fit_intercept=True)
        estimator.fit(X_train, y_train)
        estimators.append(estimator)





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

 .. code-block:: none

    Fitting model for rho=0.0
    Fitting model for rho=0.01
    Fitting model for rho=0.1




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Evaluating the models
~~~~~~~~~~~~~~~~~~~~~

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.. code-block:: Python


    # Compute the training and test errors
    train_errors = []
    test_errors = []
    for estimator in estimators:
        train_errors.append(mean_squared_error(y_train, estimator.predict(X_train)))
        test_errors.append(mean_squared_error(y_test, estimator.predict(X_test)))

    # Print the results
    for i, rho in enumerate(rhos):
        print(f'rho={rho}: training error={train_errors[i]:.2e}, test error={test_errors[i]:.2e}')





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

 .. code-block:: none

    rho=0.0: training error=1.01e-01, test error=8.27e-02
    rho=0.01: training error=1.01e-01, test error=8.26e-02
    rho=0.1: training error=1.68e-01, test error=1.25e-01




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Plotting the results
~~~~~~~~~~~~~~~~~~~~~

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.. code-block:: Python


    # Create a figure
    plt.figure()

    # Plot the training data
    plt.scatter(X_train, y_train, color='blue', label='Training data')

    # Plot the test data
    plt.scatter(X_test, y_test, color='red', label='Test data')

    # Plot the estimated models
    X_plot = np.linspace(X.min(), X.max(), 200).reshape(-1, 1)
    for i, estimator in enumerate(estimators):
        y_plot = estimator.predict(X_plot)
        plt.plot(X_plot, y_plot, label=f'rho={rhos[i]}')

    # Add labels and legend
    plt.xlabel('X')
    plt.ylabel('y')
    plt.legend()

    # Show the plot
    plt.show()









.. image-sg:: /examples/Builtin/images/sphx_glr_linear_regression_001.png
   :alt: linear regression
   :srcset: /examples/Builtin/images/sphx_glr_linear_regression_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 25.081 seconds)


.. _sphx_glr_download_examples_Builtin_linear_regression.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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