On the size of convex hulls of small sets

Shahar Mendelson

On the size of convex hulls of small sets

Shahar Mendelson

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1-18
Journal	Journal of Machine Learning Research
Volume	2
Publication status	Published - 2001

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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.",

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On the size of convex hulls of small sets

Abstract

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