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

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

.. _sphx_glr_auto_examples_plot_dirty.py:


Joint feature selection with Dirty models
=========================================

`DirtyModel` estimates a set of sparse coefficients for multiple regression
models that share a fraction of non-zero features. It is a generalization of
The `GroupLasso` estimator. It also takes a 3D `X (n_tasks, n_samples,
n_features)` and a 2D `y (n_tasks, n_samples)`.

DirtyModel solves the optimization problem::


        (1 / (2 * n_samples)) * ||Y - X(W_1 + W_2)||^2_Fro + alpha * ||W_1||_21
        + beta * ||W_2||_1

Where::

        ||W||_21 = \sum_i \sqrt{\sum_j w_ij^2}

i.e. the sum of norm of each row. and::

        ||W||_1 = \sum_i \sum_j |w_ij|



.. 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 DirtyModel







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)

    # generate random coefficients and make it sparse
    # select support
    support = rng.rand(n_features, n_tasks) > 0.95
    coef = support * rng.randn(n_features, n_tasks)

    # make features 0, 2, 4 and 6 shared
    coef[:7:2] = rng.randn(4, n_tasks)

    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)







Dirty models fit


.. code-block:: default


    alpha = 0.5
    beta = 0.25
    dirty = DirtyModel(alpha=alpha, beta=beta)
    dirty.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, dirty.coef_], ["True", "DirtyModel"]):
        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_dirty_001.png
    :class: sphx-glr-single-img




**Estimated memory usage:**  10 MB


.. _sphx_glr_download_auto_examples_plot_dirty.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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