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

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

.. _sphx_glr_auto_examples_plot_grouplasso.py:


Joint feature selection with the Group Lasso
============================================

The GroupLasso estimates a set of sparse coefficients for multiple regression
models that share the same non-zero features. All features (variable) are
either zero for all tasks or for None of them. The `GroupLasso` takes a 3D
`X (n_tasks, n_samples, n_features)` and a 2D `y (n_tasks, n_samples)`. If the
design matrix `X` of the data is the same for all tasks, we recommand using
scikit-learn's MultiTaskLasso.

The Group Lasso solves the optimization problem::


        (1 / (2 * n_samples)) * ||Y - XW||_Fro^2
        + alpha * ||W||_21




.. code-block:: default


    # Author: Hicham Janati (hicham.janati@inria.fr)
    #
    # License: BSD (3-clause)

    import numpy as np
    from matplotlib import pyplot as plt

    from mutar import GroupLasso







Generate multi-task data



.. code-block:: default


    rng = np.random.RandomState(42)
    n_tasks, n_samples, n_features = 10, 100, 30
    X = rng.randn(n_tasks, n_samples, n_features)
    coef = np.zeros((n_features, n_tasks))

    # The features 0, 2, 4, 6 are shared for all 10 tasks
    coef[:7:2] = rng.randn(4, n_tasks)

    # We pick some additional features for tasks 1 and 3
    coef[[10, 20], [1, 3]] = rng.randn(2)

    y = np.array([x.dot(c) for x, c in zip(X, coef.T)])

    # add noise
    y += 0.2 * np.std(y) + rng.randn(n_tasks, n_samples)







Group Lasso fit


.. code-block:: default


    alpha = 0.5
    gl = GroupLasso(alpha=alpha)
    gl.fit(X, y)








Plot the supports of the true and obtained coefficients.


.. code-block:: default


    f, axes = plt.subplots(1, 2, figsize=(12, 4))
    for ax, coef, name in zip(axes, [coef, gl.coef_], ["True", "GroupLasso"]):
        ax.imshow(coef != 0)
        ax.set_title(name)
        ax.set_xlabel("Tasks")
        ax.set_ylabel("Features")

    plt.show()



.. image:: /auto_examples/images/sphx_glr_plot_grouplasso_001.png
    :class: sphx-glr-single-img





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

   **Total running time of the script:** ( 0 minutes  3.641 seconds)


.. _sphx_glr_download_auto_examples_plot_grouplasso.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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