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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | print(__doc__)# Author: Alexandre Gramfort <alexandre.gramfort@inria.fr># License: BSD 3 clauseimport matplotlib.pyplot as pltimport numpy as npfrom sklearn.linear_model import MultiTaskLasso, Lassorng = np.random.RandomState(42)# Generate some 2D coefficients with sine waves with random frequency and phasen_samples, n_features, n_tasks = 100, 30, 40n_relevant_features = 5coef = 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | 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 = 0plt.figure()lw = 2plt.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() |
Total running time of the script: (0 minutes 0.320 seconds)
Download Python source code:
plot_multi_task_lasso_support.py
Download IPython notebook:
plot_multi_task_lasso_support.ipynb
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