Volume 1572 of the series Lecture Notes in Computer Science pp 274285
Generalization Performance of Classifiers in Terms of Observed Covering Numbers
 John ShaweTaylorAffiliated withDepartment of Computer Science, Royal Holloway, University of London
 , Robert C. WilliamsonAffiliated withDepartment of Engineering, Australian National University
Abstract
It is known that the covering numbers of a function class on a double sample (length 2m) can be used to bound the generalization performance of a classifier by using a margin based analysis. In this paper we show that one can utilize an analogous argument in terms of the observed covering numbers on a single msample (being the actual observed data points). The significance of this is that for certain interesting classes of functions, such as support vector machines, there are new techniques which allow one to find good estimates for such covering numbers in terms of the speed of decay of the eigenvalues of a Gram matrix. These covering numbers can be much less than a priori bounds indicate in situations where the particular data received is “easy”. The work can be considered an extension of previous results which provided generalization performance bounds in terms of the VCdimension of the class of hypotheses restricted to the sample, with the considerable advantage that the covering numbers can be readily computed, and they often are small.
 Title
 Generalization Performance of Classifiers in Terms of Observed Covering Numbers
 Book Title
 Computational Learning Theory
 Book Subtitle
 4th European Conference, EuroCOLT’99 Nordkirchen, Germany, March 29–31, 1999 Proceedings
 Pages
 pp 274285
 Copyright
 1999
 DOI
 10.1007/3540490973_22
 Print ISBN
 9783540657019
 Online ISBN
 9783540490975
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1572
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Paul Fischer ^{(1)}
 Hans Ulrich Simon ^{(2)}
 Editor Affiliations

 1. Lehrstuhl für Informatik II, Universität Dortmund
 2. Fakultät für Mathematik, Ruhr Universität Bochum
 Authors

 John ShaweTaylor ^{(5)}
 Robert C. Williamson ^{(6)}
 Author Affiliations

 5. Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, UK
 6. Department of Engineering, Australian National University, Canberra, 0200, Australia
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