.. _sphx_glr_auto_examples_linear_model_plot_lasso_coordinate_descent_path.py:


=====================
Lasso and Elastic Net
=====================

Lasso and elastic net (L1 and L2 penalisation) implemented using a
coordinate descent.

The coefficients can be forced to be positive.



.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_coordinate_descent_path_001.png
            :scale: 47

    *

      .. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_coordinate_descent_path_002.png
            :scale: 47

    *

      .. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_coordinate_descent_path_003.png
            :scale: 47


.. rst-class:: sphx-glr-script-out

 Out::

      Computing regularization path using the lasso...
    Computing regularization path using the positive lasso...
    Computing regularization path using the elastic net...
    Computing regularization path using the positive elastic net...




|


.. code-block:: python

    print(__doc__)

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

    from itertools import cycle
    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn.linear_model import lasso_path, enet_path
    from sklearn import datasets

    diabetes = datasets.load_diabetes()
    X = diabetes.data
    y = diabetes.target

    X /= X.std(axis=0)  # Standardize data (easier to set the l1_ratio parameter)

    # Compute paths

    eps = 5e-3  # the smaller it is the longer is the path

    print("Computing regularization path using the lasso...")
    alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False)

    print("Computing regularization path using the positive lasso...")
    alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
        X, y, eps, positive=True, fit_intercept=False)
    print("Computing regularization path using the elastic net...")
    alphas_enet, coefs_enet, _ = enet_path(
        X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)

    print("Computing regularization path using the positive elastic net...")
    alphas_positive_enet, coefs_positive_enet, _ = enet_path(
        X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)

    # Display results

    plt.figure(1)
    ax = plt.gca()

    colors = cycle(['b', 'r', 'g', 'c', 'k'])
    neg_log_alphas_lasso = -np.log10(alphas_lasso)
    neg_log_alphas_enet = -np.log10(alphas_enet)
    for coef_l, coef_e, c in zip(coefs_lasso, coefs_enet, colors):
        l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
        l2 = plt.plot(neg_log_alphas_enet, coef_e, linestyle='--', c=c)

    plt.xlabel('-Log(alpha)')
    plt.ylabel('coefficients')
    plt.title('Lasso and Elastic-Net Paths')
    plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
    plt.axis('tight')


    plt.figure(2)
    ax = plt.gca()
    neg_log_alphas_positive_lasso = -np.log10(alphas_positive_lasso)
    for coef_l, coef_pl, c in zip(coefs_lasso, coefs_positive_lasso, colors):
        l1 = plt.plot(neg_log_alphas_lasso, coef_l, c=c)
        l2 = plt.plot(neg_log_alphas_positive_lasso, coef_pl, linestyle='--', c=c)

    plt.xlabel('-Log(alpha)')
    plt.ylabel('coefficients')
    plt.title('Lasso and positive Lasso')
    plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
    plt.axis('tight')


    plt.figure(3)
    ax = plt.gca()
    neg_log_alphas_positive_enet = -np.log10(alphas_positive_enet)
    for (coef_e, coef_pe, c) in zip(coefs_enet, coefs_positive_enet, colors):
        l1 = plt.plot(neg_log_alphas_enet, coef_e, c=c)
        l2 = plt.plot(neg_log_alphas_positive_enet, coef_pe, linestyle='--', c=c)

    plt.xlabel('-Log(alpha)')
    plt.ylabel('coefficients')
    plt.title('Elastic-Net and positive Elastic-Net')
    plt.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
               loc='lower left')
    plt.axis('tight')
    plt.show()

**Total running time of the script:**
(0 minutes 0.377 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

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