.. _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.



.. code-block:: python

    print(__doc__)

    import numpy as np
    import matplotlib.pyplot as plt

    from sklearn.metrics import r2_score







generate some sparse data to play with


.. code-block:: python

    np.random.seed(42)

    n_samples, n_features = 50, 200
    X = np.random.randn(n_samples, n_features)
    coef = 3 * np.random.randn(n_features)
    inds = np.arange(n_features)
    np.random.shuffle(inds)
    coef[inds[10:]] = 0  # sparsify coef
    y = np.dot(X, coef)

    # add noise
    y += 0.01 * np.random.normal((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


.. code-block:: python

    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)





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

 Out::

      Lasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,
       normalize=False, positive=False, precompute=False, random_state=None,
       selection='cyclic', tol=0.0001, warm_start=False)
    r^2 on test data : 0.384710


ElasticNet


.. code-block:: python

    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)

    plt.plot(enet.coef_, color='lightgreen', linewidth=2,
             label='Elastic net coefficients')
    plt.plot(lasso.coef_, color='gold', linewidth=2,
             label='Lasso coefficients')
    plt.plot(coef, '--', color='navy', label='original coefficients')
    plt.legend(loc='best')
    plt.title("Lasso R^2: %f, Elastic Net R^2: %f"
              % (r2_score_lasso, r2_score_enet))
    plt.show()



.. image:: /auto_examples/linear_model/images/sphx_glr_plot_lasso_and_elasticnet_001.png
    :align: center


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

 Out::

      ElasticNet(alpha=0.1, copy_X=True, fit_intercept=True, l1_ratio=0.7,
          max_iter=1000, normalize=False, positive=False, precompute=False,
          random_state=None, selection='cyclic', tol=0.0001, warm_start=False)
    r^2 on test data : 0.240176


**Total running time of the script:**
(0 minutes 0.202 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

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