72 lines
2.5 KiB
Python
72 lines
2.5 KiB
Python
"""
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===============================================
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Cross-validation on diabetes Dataset Exercise
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===============================================
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A tutorial excercise which uses cross-validation with linear models.
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This exercise is used in the :ref:`cv_estimators_tut` part of the
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:ref:`model_selection_tut` section of the :ref:`stat_learn_tut_index`.
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"""
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from __future__ import print_function
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print(__doc__)
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import numpy as np
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import matplotlib.pyplot as plt
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from sklearn import cross_validation, datasets, linear_model
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diabetes = datasets.load_diabetes()
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X = diabetes.data[:150]
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y = diabetes.target[:150]
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lasso = linear_model.Lasso()
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alphas = np.logspace(-4, -.5, 30)
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scores = list()
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scores_std = list()
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for alpha in alphas:
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lasso.alpha = alpha
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this_scores = cross_validation.cross_val_score(lasso, X, y, n_jobs=1)
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scores.append(np.mean(this_scores))
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scores_std.append(np.std(this_scores))
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plt.figure(figsize=(4, 3))
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plt.semilogx(alphas, scores)
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# plot error lines showing +/- std. errors of the scores
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plt.semilogx(alphas, np.array(scores) + np.array(scores_std) / np.sqrt(len(X)),
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'b--')
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plt.semilogx(alphas, np.array(scores) - np.array(scores_std) / np.sqrt(len(X)),
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'b--')
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plt.ylabel('CV score')
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plt.xlabel('alpha')
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plt.axhline(np.max(scores), linestyle='--', color='.5')
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##############################################################################
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# Bonus: how much can you trust the selection of alpha?
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# To answer this question we use the LassoCV object that sets its alpha
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# parameter automatically from the data by internal cross-validation (i.e. it
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# performs cross-validation on the training data it receives).
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# We use external cross-validation to see how much the automatically obtained
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# alphas differ across different cross-validation folds.
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lasso_cv = linear_model.LassoCV(alphas=alphas)
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k_fold = cross_validation.KFold(len(X), 3)
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print("Answer to the bonus question:",
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"how much can you trust the selection of alpha?")
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print()
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print("Alpha parameters maximising the generalization score on different")
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print("subsets of the data:")
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for k, (train, test) in enumerate(k_fold):
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lasso_cv.fit(X[train], y[train])
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print("[fold {0}] alpha: {1:.5f}, score: {2:.5f}".
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format(k, lasso_cv.alpha_, lasso_cv.score(X[test], y[test])))
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print()
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print("Answer: Not very much since we obtained different alphas for different")
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print("subsets of the data and moreover, the scores for these alphas differ")
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print("quite substantially.")
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plt.show()
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