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"""
===========================================================
Plot Ridge coefficients as a function of the regularization
===========================================================
.. currentmodule:: sklearn.linear_model
Shows the effect of collinearity in the coefficients or the
:class:`Ridge`. At the end of the path, as alpha tends toward zero
and the solution tends towards the ordinary least squares, coefficients
exhibit big oscillations.
"""
# Author: Fabian Pedregosa -- <fabian.pedregosa@inria.fr>
# License: BSD Style.
print __doc__
import numpy as np
import pylab as pl
from sklearn import linear_model
# X is the 10x10 Hilbert matrix
X = 1. / (np.arange(1, 11) + np.arange(0, 10)[:, np.newaxis])
y = np.ones(10)
###############################################################################
# Compute paths
n_alphas = 200
alphas = np.logspace(-10, -2, n_alphas)
clf = linear_model.Ridge(fit_intercept=False)
coefs = []
for a in alphas:
clf.set_params(alpha=a)
clf.fit(X, y)
coefs.append(clf.coef_)
###############################################################################
# Display results
ax = pl.gca()
ax.set_color_cycle(['b', 'r', 'g', 'c', 'k', 'y', 'm'])
ax.plot(alphas, coefs)
ax.set_xscale('log')
ax.set_xlim(ax.get_xlim()[::-1]) # reverse axis
pl.xlabel('alpha')
pl.ylabel('weights')
pl.title('Ridge coefficients as a function of the regularization')
pl.axis('tight')
pl.show()
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