Cross-validation on diabetes Dataset Exercise

A tutorial excercise which uses cross-validation with linear models.

This exercise is used in the Cross-validated estimators part of the Model selection: choosing estimators and their parameters section of the A tutorial on statistical-learning for scientific data processing.

Python source code: plot_cv_diabetes.py

from __future__ import print_function

import numpy as np
import pylab as pl

from sklearn import cross_validation, datasets, linear_model

print(__doc__)

diabetes = datasets.load_diabetes()
X = diabetes.data[:150]
y = diabetes.target[:150]

lasso = linear_model.Lasso()

alphas = np.logspace(-4, -.5, 30)

scores = list()
scores_std = list()

for alpha in alphas:
    lasso.alpha = alpha
    this_scores = cross_validation.cross_val_score(lasso, X, y, n_jobs=1)
    scores.append(np.mean(this_scores))
    scores_std.append(np.std(this_scores))

pl.figure(figsize=(4, 3))
pl.semilogx(alphas, scores)
# plot error lines showing +/- std. errors of the scores
pl.semilogx(alphas, np.array(scores) + np.array(scores_std) / np.sqrt(len(X)),
            'b--')
pl.semilogx(alphas, np.array(scores) - np.array(scores_std) / np.sqrt(len(X)),
            'b--')
pl.ylabel('CV score')
pl.xlabel('alpha')
pl.axhline(np.max(scores), linestyle='--', color='.5')

##############################################################################
# Bonus: how much can you trust the selection of alpha?

# To answer this question we use the LassoCV object that sets its alpha
# parameter automatically from the data by internal cross-validation (i.e. it
# performs cross-validation on the training data it receives).
# We use external cross-validation to see how much the automatically obtained
# alphas differ across different cross-validation folds.
lasso_cv = linear_model.LassoCV(alphas=alphas)
k_fold = cross_validation.KFold(len(X), 3)

print("Answer to the bonus question:",
      "how much can you trust the selection of alpha?")
print()
print("Alpha parameters maximising the generalization score on different")
print("subsets of the data:")
for k, (train, test) in enumerate(k_fold):
    lasso_cv.fit(X[train], y[train])
    print("[fold {0}] alpha: {1:.5f}, score: {2:.5f}".
          format(k, lasso_cv.alpha_, lasso_cv.score(X[test], y[test])))
print()
print("Answer: Not very much since we obtained different alphas for different")
print("subsets of the data and moreover, the scores for these alphas differ")
print("quite substantially.")

pl.show()