Exact combinatorial bounds on the probability of overfitting for empirical risk minimization |
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Authors: | K V Vorontsov |
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Affiliation: | 1.Dorodnicyn Computing Centre,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | Three general methods for obtaining exact bounds on the probability of overfitting are proposed within statistical learning
theory: a method of generating and destroying sets, a recurrent method, and a blockwise method. Six particular cases are considered
to illustrate the application of these methods. These are the following model sets of predictors: a pair of predictors, a
layer of a Boolean cube, an interval of a Boolean cube, a monotonic chain, a unimodal chain, and a unit neighborhood of the
best predictor. For the interval and the unimodal chain, the results of numerical experiments are presented that demonstrate
the effects of splitting and similarity on the probability of overfitting. |
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Keywords: | |
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