.. _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 # 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 0.314 seconds) .. container:: sphx-glr-download **Download Python source code:** :download:`plot_multi_task_lasso_support.py ` .. container:: sphx-glr-download **Download IPython notebook:** :download:`plot_multi_task_lasso_support.ipynb `