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.
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, 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
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)
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
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()
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 0.203 seconds)
Download Python source code:
plot_lasso_and_elasticnet.py
Download IPython notebook:
plot_lasso_and_elasticnet.ipynb
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