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

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

.. _sphx_glr_auto_examples_plot_compare_rvr_ard.py:


=====================================================================
Comparison of relevance vector regression and ARDRegression
=====================================================================

Based on https://scikit-learn.org/stable/auto_examples/linear_model/plot_ard.html#sphx-glr-auto-examples-linear-model-plot-ard-py



.. image:: /auto_examples/images/sphx_glr_plot_compare_rvr_ard_001.png
    :class: sphx-glr-single-img






.. code-block:: default

    print(__doc__)

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import stats
    from sklearn.linear_model import ARDRegression
    from sklearn_rvm import EMRVR

    # #############################################################################
    # Generating simulated data with Gaussian weights

    # Parameters of the example
    np.random.seed(0)

    n_samples, n_features = 100, 100

    # Create Gaussian data
    X = np.random.randn(n_samples, n_features)
    # Create weights with a precision lambda_ of 4.
    lambda_ = 4.
    w = np.zeros(n_features)
    # Only keep 10 weights of interest
    relevant_features = np.random.randint(0, n_features, 10)
    for i in relevant_features:
        w[i] = stats.norm.rvs(loc=0, scale=1. / np.sqrt(lambda_))
    # Create noise with a precision alpha of 50.
    alpha_ = 50.
    noise = stats.norm.rvs(loc=0, scale=1. / np.sqrt(alpha_), size=n_samples)
    # Create the target
    y = np.dot(X, w) + noise

    # #############################################################################
    # Fit the ARD Regression
    clf = ARDRegression(compute_score=True)
    clf.fit(X, y)

    rvr = EMRVR(kernel="linear")
    rvr.fit(X, y)

    # #############################################################################
    # Plot the true weights, the estimated weights, the histogram of the
    # weights, and predictions with standard deviations
    plt.figure(figsize=(6, 5))
    plt.title("Weights of the model")
    plt.plot(rvr.coef_, color="darkblue", linestyle="-", linewidth=2, label="RVR estimate")
    plt.plot(clf.coef_, color="yellowgreen", linestyle=":", linewidth=2, label="ARD estimate")
    plt.plot(w, color="orange", linestyle="-", linewidth=2, label="Ground truth")
    plt.xlabel("Features")
    plt.ylabel("Values of the weights")
    plt.legend(loc=1)
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  17.338 seconds)


.. _sphx_glr_download_auto_examples_plot_compare_rvr_ard.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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