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2001 JMLR JMLR 2001

On the Size of Convex Hulls of Small Sets

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. [abs] [pdf] [ps.gz] [ps]

🌱 Topic Pioneer — Learning Theory
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Authors

Shahar Mendelson

Topics

Machine Learning > Optimization & Theory > Learning Theory Machine Learning > Optimization & Theory > Statistical Learning Machine Learning > Optimization & Theory > Theory Machine Learning > Core Methods > Dimensionality Reduction

Keywords

learning theory fat-shattering dimension convex hull covering number
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