def test_lasso_path():
# build an ill-posed linear regression problem with many noisy features and
# comparatively few samples
n_samples, n_features, maxit = 50, 200, 30
np.random.seed(0)
w = np.random.randn(n_features)
w[10:] = 0.0 # only the top 10 features are impacting the model
X = np.random.randn(n_samples, n_features)
y = np.dot(X, w)
clf = LassoCV(n_alphas=100, eps=1e-3).fit(X, y, maxit=maxit)
assert_almost_equal(clf.alpha, 0.011, 2)
# test set
X_test = np.random.randn(n_samples, n_features)
y_test = np.dot(X_test, w)
rmse = np.sqrt(((y_test - clf.predict(X_test)) ** 2).mean())
assert_almost_equal(rmse, 0.062, 2)
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)
