A note on different covering numbers in learning theory

被引：26
|
作者：
Pontil, M [1 ]
机构：
[1] UCL, Dept Comp Sci, London WC1E, England
来源：
JOURNAL OF COMPLEXITY | 2003年 / 19卷 / 05期
关键词：
D O I：
10.1016/S0885-064X(03)00033-5
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
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).
引用
收藏
页码：665 / 671
页数：7
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