Ridge regression scaled

scale_c_ridge.py

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

"""
=========================================================
Title
=========================================================
Description

"""
print __doc__


# Author: Andreas Mueller <amueller@ais.uni-bonn.de>
#         Jaques Grobler <jaques.grobler@inria.fr>
# License: BSD



import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import Ridge
from sklearn.cross_validation import ShuffleSplit
from sklearn.grid_search import GridSearchCV
from sklearn.utils import check_random_state
from time import time

if __name__ == '__main__':
    rnd = check_random_state(1)

    # set up dataset
    n_samples = 100
    n_features = 1000
    subplotnum = 1

    X = rnd.randn(n_samples, n_features)
    coef = 5 * rnd.randn(n_features)
    # coef[10:] = 0

    y = np.dot(X, coef)

    clf = Ridge(fit_intercept=False, tol=0.1)

    alphas = np.logspace(-2, 6, 30)

    t0_clf = time()
    plt.figure(figsize=(9, 10))
    plt.clf()
    plt.xlabel('C')
    plt.ylabel('CV Score')

    colors = ['b', 'g', 'r', 'c']

    for k, train_fraction in enumerate(np.arange(0.2, 0.6, 0.1)[::-1]):
        param_grid = dict(alpha=alphas)
        t0 = time()
        grid = GridSearchCV(clf, n_jobs=-1, refit=False, param_grid=param_grid,
                            cv=ShuffleSplit(n=n_samples, train_fraction=train_fraction,
                                            n_iterations=100, random_state=1))
        grid.fit(X, y)
        print "GridSearchCV done in %0.3fs." % (time() - t0)
        scores = [x[1] for x in grid.grid_scores_]
        print(clf)
        scales = [(1, 'No scaling'),
                  (1./(np.sqrt(n_samples * train_fraction)), '1/sqrt(n_samples)'),
                  (1./(n_samples * train_fraction), '1/n_samples'),
                  ]

        for subplotnum, (scaler, name) in enumerate(scales):
            print ('%s: Scaler: %s (1/%s)') % (subplotnum + 1, name, scaler)
            plt.subplot(3, 1, subplotnum + 1)

            grid_alphas = alphas / float(scaler)

            plt.semilogx(grid_alphas, scores,
                            label="fraction %.2f" % train_fraction)
            ymin, ymax = plt.ylim()
            plt.vlines(grid_alphas[np.argmax(scores)], ymin, ymax,
                       color=colors[k], linestyles='solid')

        print '-------------------------------'

        # plot ledgend
        plt.legend(loc="lower left")
        print "Total time taken: %0.3fs." % (time() - t0_clf)
    plt.show()
    print "Completed"