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2010 | 20 | 3 | 525-544
Tytuł artykułu

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic probabilities of discrepancy between these minima for given for given conditions of an experiment. The probabilities are calculated in terms of all relevant constants: the sample size, the number of cross-validation folds, the capacity of the set of approximating functions and bounds on this set. We report experiments carried out to validate the results.
Rocznik
Tom
20
Numer
3
Strony
525-544
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-06-19
poprawiono
2010-03-16
poprawiono
2010-03-19
Twórcy
  • Department of Methods of Artificial Intelligence and Applied Mathematics, Westpomeranian University of Technology, ul. Żołnierska 49, 71-210 Szczecin, Poland
Bibliografia
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Typ dokumentu
Bibliografia
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