.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples\LinearModels\LocallyWeightedRegression.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_LinearModels_LocallyWeightedRegression.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_LinearModels_LocallyWeightedRegression.py:


Locally Weighted Regression on a Sine Function
==============================================

This script demonstrates Locally Weighted Regression (LWR), using a Gaussian kernel 
to assign weights to training samples based on their distance from a test 
point.

.. GENERATED FROM PYTHON SOURCE LINES 9-50



.. image-sg:: /auto_examples/LinearModels/images/sphx_glr_LocallyWeightedRegression_001.png
   :alt: Tau = 0.203 - R2 = 0.906, Tau = 0.251 - R2 = 0.904, Tau = 0.31 - R2 = 0.901, Tau = 0.384 - R2 = 0.894, Tau = 0.475 - R2 = 0.881, Tau = 0.587 - R2 = 0.855, Tau = 0.727 - R2 = 0.807, Tau = 0.899 - R2 = 0.725, Tau = 1.112 - R2 = 0.61, Tau = 1.376 - R2 = 0.495, Tau = 1.702 - R2 = 0.408, Tau = 2.106 - R2 = 0.348, Tau = 2.605 - R2 = 0.301, Tau = 3.223 - R2 = 0.263, Tau = 3.988 - R2 = 0.232, Tau = 4.933 - R2 = 0.207
   :srcset: /auto_examples/LinearModels/images/sphx_glr_LocallyWeightedRegression_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import torch
    import matplotlib.pyplot as plt

    from DLL.MachineLearning.SupervisedLearning.LinearModels import LinearRegression
    from DLL.Data.Metrics import r2_score
    from DLL.Data.Preprocessing import data_split


    X = torch.linspace(0, 2 * torch.pi, 1000).unsqueeze(1)
    y = torch.sin(X).squeeze() + 0.2 * torch.randn_like(X.squeeze())
    X_train, y_train, X_test, y_test, _, _ = data_split(X, y)

    def get_weight(train, test, tau):
        d2 = torch.sum((train - test) ** 2, dim=1)
        w = torch.exp(-d2 / (2. * tau * tau))
        return w

    def get_pred(tau):
        y_pred = []
        for test_point in X_test:
            weight = get_weight(X_train, test_point, tau)
            model = LinearRegression()
            model.fit(X_train, y_train, sample_weight=weight)
            y_pred.append(model.predict(test_point.reshape(1, -1))[0])

        y_pred = torch.stack(y_pred).reshape(-1,)
        return y_pred

    n = 4
    m = 4
    fig, axes = plt.subplots(m, n, figsize=(15, 10))
    plt.subplots_adjust(hspace=0.5)
    axes = axes.ravel()
    taus = torch.logspace(torch.log(torch.Tensor([0.5]).squeeze()), torch.log(torch.Tensor([2.0]).squeeze()), m * n)
    for i, ax in enumerate(axes):
        y_pred = get_pred(taus[i])
        ax.set_title(f"Tau = {round(taus[i].item(), 3)} - R2 = {round(r2_score(y_test, y_pred), 3)}")
        ax.scatter(X_test, y_pred, s=10, c="r", label="prediction")
        ax.scatter(X_test, y_test, s=10, c="b", label="true")
        ax.grid()
    plt.show()


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

   **Total running time of the script:** (0 minutes 9.062 seconds)


.. _sphx_glr_download_auto_examples_LinearModels_LocallyWeightedRegression.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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