.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_auto_examples_linear_model_plot_lasso_and_elasticnet.py>` to download the full example code or to run this example in your browser via Binder
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_linear_model_plot_lasso_and_elasticnet.py:


========================================
Lasso and Elastic Net for Sparse Signals
========================================

Estimates Lasso and Elastic-Net regression models on a manually generated
sparse signal corrupted with an additive noise. Estimated coefficients are
compared with the ground-truth.



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_and_elasticnet_001.png
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    Lasso(alpha=0.1)
    r^2 on test data : 0.658064
    ElasticNet(alpha=0.1, l1_ratio=0.7)
    r^2 on test data : 0.642515






|


.. code-block:: default

    print(__doc__)

    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn.metrics import r2_score

    # #############################################################################
    # Generate some sparse data to play with
    np.random.seed(42)

    n_samples, n_features = 50, 100
    X = np.random.randn(n_samples, n_features)

    # Decreasing coef w. alternated signs for visualization
    idx = np.arange(n_features)
    coef = (-1) ** idx * np.exp(-idx / 10)
    coef[10:] = 0  # sparsify coef
    y = np.dot(X, coef)

    # Add noise
    y += 0.01 * np.random.normal(size=n_samples)

    # Split data in train set and test set
    n_samples = X.shape[0]
    X_train, y_train = X[:n_samples // 2], y[:n_samples // 2]
    X_test, y_test = X[n_samples // 2:], y[n_samples // 2:]

    # #############################################################################
    # Lasso
    from sklearn.linear_model import Lasso

    alpha = 0.1
    lasso = Lasso(alpha=alpha)

    y_pred_lasso = lasso.fit(X_train, y_train).predict(X_test)
    r2_score_lasso = r2_score(y_test, y_pred_lasso)
    print(lasso)
    print("r^2 on test data : %f" % r2_score_lasso)

    # #############################################################################
    # ElasticNet
    from sklearn.linear_model import ElasticNet

    enet = ElasticNet(alpha=alpha, l1_ratio=0.7)

    y_pred_enet = enet.fit(X_train, y_train).predict(X_test)
    r2_score_enet = r2_score(y_test, y_pred_enet)
    print(enet)
    print("r^2 on test data : %f" % r2_score_enet)

    m, s, _ = plt.stem(np.where(enet.coef_)[0], enet.coef_[enet.coef_ != 0],
                       markerfmt='x', label='Elastic net coefficients',
                       use_line_collection=True)
    plt.setp([m, s], color="#2ca02c")
    m, s, _ = plt.stem(np.where(lasso.coef_)[0], lasso.coef_[lasso.coef_ != 0],
                       markerfmt='x', label='Lasso coefficients',
                       use_line_collection=True)
    plt.setp([m, s], color='#ff7f0e')
    plt.stem(np.where(coef)[0], coef[coef != 0], label='true coefficients',
             markerfmt='bx', use_line_collection=True)

    plt.legend(loc='best')
    plt.title("Lasso $R^2$: %.3f, Elastic Net $R^2$: %.3f"
              % (r2_score_lasso, r2_score_enet))
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.552 seconds)

**Estimated memory usage:**  8 MB


.. _sphx_glr_download_auto_examples_linear_model_plot_lasso_and_elasticnet.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example


  .. container:: binder-badge

    .. image:: https://mybinder.org/badge_logo.svg
      :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.22.X?urlpath=lab/tree/notebooks/auto_examples/linear_model/plot_lasso_and_elasticnet.ipynb
      :width: 150 px


  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_lasso_and_elasticnet.py <plot_lasso_and_elasticnet.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_lasso_and_elasticnet.ipynb <plot_lasso_and_elasticnet.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_