.. 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

        :ref:`Go to the end <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 JupyterLite or 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 15-19

.. code-block:: Python


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








.. GENERATED FROM PYTHON SOURCE LINES 20-22

Generate data
-------------

.. GENERATED FROM PYTHON SOURCE LINES 22-38

.. code-block:: Python


    import numpy as np

    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((1.0 + 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)








.. GENERATED FROM PYTHON SOURCE LINES 39-41

Fit models
----------

.. GENERATED FROM PYTHON SOURCE LINES 41-47

.. code-block:: Python


    from sklearn.linear_model import Lasso, MultiTaskLasso

    coef_lasso_ = np.array([Lasso(alpha=0.5).fit(X, y).coef_ for y in Y.T])
    coef_multi_task_lasso_ = MultiTaskLasso(alpha=1.0).fit(X, Y).coef_








.. GENERATED FROM PYTHON SOURCE LINES 48-50

Plot support and time series
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 50-83

.. code-block:: Python


    import matplotlib.pyplot as plt

    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-horizontal


    *

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

    *

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






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

   **Total running time of the script:** (0 minutes 0.268 seconds)


.. _sphx_glr_download_auto_examples_linear_model_plot_multi_task_lasso_support.py:

.. only:: html

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

    .. container:: binder-badge

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../lite/lab/?path=auto_examples/linear_model/plot_multi_task_lasso_support.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

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

    .. 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>`


.. include:: plot_multi_task_lasso_support.recommendations


.. only:: html

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

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