Lasso parameter estimation with path and cross-validation

Python source code: lasso_path_with_crossvalidation.py

import numpy as np

################################################################################
# generate some sparse data to play with

n_samples, n_features = 60, 100

np.random.seed(1)
X = np.random.randn(n_samples, n_features)
coef = 3*np.random.randn(n_features)
coef[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
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 with path and cross-validation using LassoCV path
from scikits.learn.glm import LassoCV
from scikits.learn.cross_val import KFold

cv = KFold(n_samples/2, 5)
lasso_cv = LassoCV()

# fit_params = {'maxit':100}

y_ = lasso_cv.fit(X_train, y_train, cv=cv, maxit=100).predict(X_test)

print "Optimal regularization parameter  = %s" % lasso_cv.alpha

# Compute explained variance on test data
print "r^2 on test data : %f" % (1 - np.linalg.norm(y_test - y_)**2
                                      / np.linalg.norm(y_test)**2)