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

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

.. _sphx_glr_auto_examples_LinearModels_RANSAC.py:


Robust Regression with RANSAC
================================

This script demonstrates the use of RANSAC (Random Sample Consensus) regression to fit a robust model in the presence of outliers.
A quadratic relationship is used to generate inlier data, while a separate set of points acts as outliers. The performance of standard
linear regression is compared with RANSAC regression to highlight the latter's robustness to noisy data.

- Inliers follow the function: \( y = 2x^2 + 1 +        ext{noise} \)
- Outliers are randomly distributed and do not follow the quadratic trend.
- A polynomial feature transformation is applied to the input data to allow for quadratic regression.

.. GENERATED FROM PYTHON SOURCE LINES 13-43



.. image-sg:: /auto_examples/LinearModels/images/sphx_glr_RANSAC_001.png
   :alt: RANSAC
   :srcset: /auto_examples/LinearModels/images/sphx_glr_RANSAC_001.png
   :class: sphx-glr-single-img





.. code-block:: Python

    import torch
    import matplotlib.pyplot as plt

    from DLL.MachineLearning.SupervisedLearning.LinearModels import LinearRegression, RANSACRegression
    from DLL.Data.Preprocessing import PolynomialFeatures


    num_inliers = 100
    num_outliers = 20

    x_inliers = torch.linspace(0, 10, num_inliers)
    y_inliers = 2 * x_inliers ** 2 + 1 + torch.randn(num_inliers)
    x_outliers = torch.rand(num_outliers) * 4 + 6
    y_outliers = torch.rand(num_outliers) * 20 + 10
    X = PolynomialFeatures(degree=2).transform(torch.cat((x_inliers, x_outliers)).unsqueeze(-1))
    y = torch.cat((y_inliers, y_outliers))
    indices = torch.randperm(len(X))
    X, y = X[indices], y[indices]

    lr = LinearRegression()
    lr.fit(X, y)
    ransac = RANSACRegression(estimator=LinearRegression())
    ransac.fit(X, y, min_samples=0.1)

    plt.plot(x_inliers, y_inliers, ".", label="inliers")
    plt.plot(x_outliers, y_outliers, ".", label="outliers")
    plt.plot(x_inliers, lr.predict(PolynomialFeatures(degree=2).transform(x_inliers.unsqueeze(-1))), label="Linear regression")
    plt.plot(x_inliers, ransac.predict(PolynomialFeatures(degree=2).transform(x_inliers.unsqueeze(-1))), label="RANSAC regression")
    plt.legend()
    plt.show()


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

   **Total running time of the script:** (0 minutes 1.560 seconds)


.. _sphx_glr_download_auto_examples_LinearModels_RANSAC.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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