Note
Click here to download the full example code
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.
Out:
Optimal regularization parameter : 0.000335292414924956
print(__doc__) # Author: Alexandre Gramfort <[email protected]> # License: BSD 3 clause import numpy as np from sklearn import linear_model # ############################################################################# # Generate sample data 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 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 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 3.788 seconds)
Gallery generated by Sphinx-Gallery
© 2007–2018 The scikit-learn developers
Licensed under the 3-clause BSD License.
http://scikit-learn.org/stable/auto_examples/model_selection/plot_train_error_vs_test_error.html