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2 Klęsk P.

2 2010

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A comparison of certain generalization bounds of learning machines for practical applications

Klęsk P.

Metody Informatyki Stosowanej

2010

nr 4 (24)

35-45

In statisticallearning bounds on generalization error and sample complexities are important elements. In the paper we compare several selected generalization bounds having in mind their practical applications. In particular; we state twa theorems which compare bounds derived via additive and multiplicative versions of Chemoff inequality. In experimental part we show (using a benchmark data set) how one can practically apply bounds and sample complexity.

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

Klęsk P.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 3

525-544

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.