On the size of convex hulls of small sets

Authors:
Shahar Mendelson
Affiliations:
Computer Sciences Laboratory, Research School of Information Sciences and Engineering, The Australian National University, Canberra 0200, Australia
Venue:
The Journal of Machine Learning Research
Year:
2002

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Abstract

We investigate two different notions of "size" which appear naturally in Statistical Learning Theory. We present quantitative estimates on the fat-shattering dimension and on the covering numbers of convex hulls of sets of functions, given the necessary data on the original sets. The proofs we present are relatively simple since they do not require extensive background in convex geometry.