scikit-learn/examples/tutorial/plot_ridge_variance.py

#!/usr/bin/python
# -*- coding: utf-8 -*-

"""
=========================================================
Ridge Regression Variance Example
=========================================================
Ridge regression is basically minimizing a penalised version
of the least-squared function. The penalising `shrinks` the
value of the regression coefficients.
Despite the few data points in each dimension, the slope
of the prediction is much more stable and the variance
in the line itself is greatly reduced, in comparison to that
of the standard linear regression
"""
print __doc__


# Code source: Gael Varoqueux
# Modified for Documentation merge by Jaques Grobler
# License: BSD


import numpy as np
import pylab as pl

from sklearn import linear_model

X_train = np.c_[ .5, 1].T
y_train = [.5, 1]
X_test = np.c_[ 0, 2].T

fig = pl.figure(1, figsize=(4, 3))
pl.clf()
ax = pl.axes([.12, .12, .8, .8])

np.random.seed(0)
ridge = linear_model.Ridge(alpha=.1)

for _ in range(6):
    this_X = .1*np.random.normal(size=(2, 1)) + X_train
    ridge.fit(this_X, y_train)

    ax.plot(X_test, ridge.predict(X_test), color='.5')
    ax.scatter(this_X, y_train, s=3, c='.5', marker='o', zorder=10)

ridge.fit(X_train, y_train)

ax.plot(X_test, ridge.predict(X_test), linewidth=2, color='blue')
ax.scatter(X_train, y_train, s=30, c='r', marker='+', zorder=10)

ax.set_xticks(())
ax.set_yticks(())
ax.set_xlabel('X')
ax.set_ylabel('y')
ax.set_xlim(0, 2)

pl.show()