A note on different covering numbers in learning theory

Authors:
Massimiliano Pontil
Affiliations:
Department of Computer Sciences, University College London, Gower Street, London WC1E, UK
Venue:
Journal of Complexity
Year:
2003

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Abstract

The covering number of a set F in the space of continuous functions on a compact set X plays an important role in learning theory. In this paper, we study the relation between this covering number and its discrete version, obtained by replacing X with a finite subset. We formally show that when F is made of smooth functions, the discrete covering number is close to its continuous counterpart. In particular, we illustrate this result in the case that F is a ball in a reproducing kernel Hilbert space.