# A RELATIONSHIP BETWEEN CROSS-VALIDATION AND VAPNIK BOUNDS ON GENERALIZATION OF LEARNING MACHINES

### Przemysław Klęsk

#### Abstract

Typically, the n-fold cross-validation is used both to: (1) estimate the generalization properties of a model of fixed complexity, (2) choose from a family of models of different complexities, the one with the best complexity, given a data set of certain size. Obviously, it is a time-consuming procedure. A different approach — the Structural Risk Minimization is based on generalization bounds of learning machines given by Vapnik (Vapnik, 1995a; Vapnik, 1995b). Roughly speaking, SRM is O(n) times faster than n-fold cross-validation but less accurate. We state and prove theorems, which show the probabilistic relationship between the two approaches. In particular, we show what e-difference between the two, one may expect without actually performing the crossvalidation. We conclude the paper with results of experiments confronting the probabilistic bounds we derived.

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#### Paper Citation

#### in Harvard Style

Klęsk P. (2011). **A RELATIONSHIP BETWEEN CROSS-VALIDATION AND VAPNIK BOUNDS ON GENERALIZATION OF LEARNING MACHINES** . In *Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,* ISBN 978-989-8425-40-9, pages 5-17. DOI: 10.5220/0003121000050017

#### in Bibtex Style

@conference{icaart11,

author={Przemysław Klęsk},

title={A RELATIONSHIP BETWEEN CROSS-VALIDATION AND VAPNIK BOUNDS ON GENERALIZATION OF LEARNING MACHINES},

booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},

year={2011},

pages={5-17},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003121000050017},

isbn={978-989-8425-40-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,

TI - A RELATIONSHIP BETWEEN CROSS-VALIDATION AND VAPNIK BOUNDS ON GENERALIZATION OF LEARNING MACHINES

SN - 978-989-8425-40-9

AU - Klęsk P.

PY - 2011

SP - 5

EP - 17

DO - 10.5220/0003121000050017