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A note on different covering numbers in learning theory

Pontil, M; (2003) A note on different covering numbers in learning theory. J COMPLEXITY , 19 (5) 665 - 671. 10.1016/S0885-064X(03)00033-5.

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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. (C) 2003 Published by Elsevier Science (USA).

Type:Article
Title:A note on different covering numbers in learning theory
DOI:10.1016/S0885-064X(03)00033-5
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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