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scikit-learn 1.3.2
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# 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.

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

## Generate data

    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)

## Fit models

    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_

## Plot support and time series

    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()

Total running time of the script: (0 minutes 0.162 seconds)

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