"""
==================================================
Cross validated Lasso path with coordinate descent
==================================================

Compute a 5-fold cross-validated Lasso path with coordinate descent to find the
optimal value of alpha.
"""
print __doc__

# Author: Olivier Grisel
# License: BSD Style.

import numpy as np
import pylab as pl

from scikits.learn.linear_model import LassoCV
from scikits.learn import datasets

diabetes = datasets.load_diabetes()
X = diabetes.data
y = diabetes.target

# normalize data as done by LARS to allow for comparison
X /= np.sqrt(np.sum(X ** 2, axis=0))

##############################################################################
# Compute paths

eps = 1e-3 # the smaller it is the longer is the path

print "Computing regularization path using the lasso..."
model = LassoCV(eps=eps).fit(X, y)

##############################################################################
# Display results
m_log_alphas = -np.log10(model.alphas)
m_log_alpha = -np.log10(model.alpha)

ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
pl.subplot(2, 1, 1)
pl.plot(m_log_alphas, model.coef_path_)

ymin, ymax = pl.ylim()
pl.vlines([m_log_alpha], ymin, ymax, linestyle='dashed')

pl.xticks(())
pl.ylabel('weights')
pl.title('Lasso paths')
pl.axis('tight')

pl.subplot(2, 1, 2)
ymin, ymax = 2600, 3800
pl.plot(m_log_alphas, model.mse_path_)
pl.vlines([m_log_alpha], ymin, ymax, linestyle='dashed')

pl.xlabel('-log(lambda)')
pl.ylabel('MSE')
pl.title('Mean Square Errors on each CV fold')
pl.axis('tight')
pl.ylim(ymin, ymax)

pl.show()