.. _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.



.. code-block:: python

    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


.. code-block:: python

    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:: /auto_examples/linear_model/images/sphx_glr_plot_multi_task_lasso_support_001.png
            :scale: 47

    *

      .. image:: /auto_examples/linear_model/images/sphx_glr_plot_multi_task_lasso_support_002.png
            :scale: 47




**Total running time of the script:**
(0 minutes 0.320 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

    **Download IPython notebook:** :download:`plot_multi_task_lasso_support.ipynb <plot_multi_task_lasso_support.ipynb>`