

.. _sphx_glr_auto_examples_model_selection_plot_train_error_vs_test_error.py:


=========================
Train error vs Test error
=========================

Illustration of how the performance of an estimator on unseen data (test data)
is not the same as the performance on training data. As the regularization
increases the performance on train decreases while the performance on test
is optimal within a range of values of the regularization parameter.
The example with an Elastic-Net regression model and the performance is
measured using the explained variance a.k.a. R^2.



.. code-block:: python

    print(__doc__)

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

    import numpy as np
    from sklearn import linear_model


Generate sample data


.. code-block:: python

    n_samples_train, n_samples_test, n_features = 75, 150, 500
    np.random.seed(0)
    coef = np.random.randn(n_features)
    coef[50:] = 0.0  # only the top 10 features are impacting the model
    X = np.random.randn(n_samples_train + n_samples_test, n_features)
    y = np.dot(X, coef)

    # Split train and test data
    X_train, X_test = X[:n_samples_train], X[n_samples_train:]
    y_train, y_test = y[:n_samples_train], y[n_samples_train:]


Compute train and test errors


.. code-block:: python

    alphas = np.logspace(-5, 1, 60)
    enet = linear_model.ElasticNet(l1_ratio=0.7)
    train_errors = list()
    test_errors = list()
    for alpha in alphas:
        enet.set_params(alpha=alpha)
        enet.fit(X_train, y_train)
        train_errors.append(enet.score(X_train, y_train))
        test_errors.append(enet.score(X_test, y_test))

    i_alpha_optim = np.argmax(test_errors)
    alpha_optim = alphas[i_alpha_optim]
    print("Optimal regularization parameter : %s" % alpha_optim)

    # Estimate the coef_ on full data with optimal regularization parameter
    enet.set_params(alpha=alpha_optim)
    coef_ = enet.fit(X, y).coef_


Plot results functions


.. code-block:: python


    import matplotlib.pyplot as plt
    plt.subplot(2, 1, 1)
    plt.semilogx(alphas, train_errors, label='Train')
    plt.semilogx(alphas, test_errors, label='Test')
    plt.vlines(alpha_optim, plt.ylim()[0], np.max(test_errors), color='k',
               linewidth=3, label='Optimum on test')
    plt.legend(loc='lower left')
    plt.ylim([0, 1.2])
    plt.xlabel('Regularization parameter')
    plt.ylabel('Performance')

    # Show estimated coef_ vs true coef
    plt.subplot(2, 1, 2)
    plt.plot(coef, label='True coef')
    plt.plot(coef_, label='Estimated coef')
    plt.legend()
    plt.subplots_adjust(0.09, 0.04, 0.94, 0.94, 0.26, 0.26)
    plt.show()

**Total running time of the script:**
(0 minutes 0.000 seconds)



.. container:: sphx-glr-download

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


.. container:: sphx-glr-download

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