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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_linear_model_plot_multi_task_lasso_support.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_linear_model_plot_multi_task_lasso_support.py:


=============================================
Joint feature selection with multi-task Lasso
=============================================

The multi-task lasso allows to fit multiple regression problems
jointly enforcing the selected features to be the same across
tasks. This example simulates sequential measurements, each task
is a time instant, and the relevant features vary in amplitude
over time while being the same. The multi-task lasso imposes that
features that are selected at one time point are select for all time
point. This makes feature selection by the Lasso more stable.

.. GENERATED FROM PYTHON SOURCE LINES 16-70



.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /auto_examples/linear_model/images/sphx_glr_plot_multi_task_lasso_support_001.png
          :alt: Coefficient non-zero location
          :class: sphx-glr-multi-img

    *

      .. image:: /auto_examples/linear_model/images/sphx_glr_plot_multi_task_lasso_support_002.png
          :alt: plot multi task lasso support
          :class: sphx-glr-multi-img





.. code-block:: default

    print(__doc__)

    # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
    # License: BSD 3 clause

    import matplotlib.pyplot as plt
    import numpy as np

    from sklearn.linear_model import MultiTaskLasso, Lasso

    rng = np.random.RandomState(42)

    # Generate some 2D coefficients with sine waves with random frequency and phase
    n_samples, n_features, n_tasks = 100, 30, 40
    n_relevant_features = 5
    coef = np.zeros((n_tasks, n_features))
    times = np.linspace(0, 2 * np.pi, n_tasks)
    for k in range(n_relevant_features):
        coef[:, k] = np.sin((1. + rng.randn(1)) * times + 3 * rng.randn(1))

    X = rng.randn(n_samples, n_features)
    Y = np.dot(X, coef.T) + rng.randn(n_samples, n_tasks)

    coef_lasso_ = np.array([Lasso(alpha=0.5).fit(X, y).coef_ for y in Y.T])
    coef_multi_task_lasso_ = MultiTaskLasso(alpha=1.).fit(X, Y).coef_

    # #############################################################################
    # Plot support and time series
    fig = plt.figure(figsize=(8, 5))
    plt.subplot(1, 2, 1)
    plt.spy(coef_lasso_)
    plt.xlabel('Feature')
    plt.ylabel('Time (or Task)')
    plt.text(10, 5, 'Lasso')
    plt.subplot(1, 2, 2)
    plt.spy(coef_multi_task_lasso_)
    plt.xlabel('Feature')
    plt.ylabel('Time (or Task)')
    plt.text(10, 5, 'MultiTaskLasso')
    fig.suptitle('Coefficient non-zero location')

    feature_to_plot = 0
    plt.figure()
    lw = 2
    plt.plot(coef[:, feature_to_plot], color='seagreen', linewidth=lw,
             label='Ground truth')
    plt.plot(coef_lasso_[:, feature_to_plot], color='cornflowerblue', linewidth=lw,
             label='Lasso')
    plt.plot(coef_multi_task_lasso_[:, feature_to_plot], color='gold', linewidth=lw,
             label='MultiTaskLasso')
    plt.legend(loc='upper center')
    plt.axis('tight')
    plt.ylim([-1.1, 1.1])
    plt.show()


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

   **Total running time of the script:** ( 0 minutes  0.338 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_multi_task_lasso_support.py:


.. only :: html

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


  .. container:: binder-badge

    .. image:: images/binder_badge_logo.svg
      :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.24.X?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_multi_task_lasso_support.ipynb
      :alt: Launch binder
      :width: 150 px


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

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



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

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


.. only:: html

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

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