VC bounds on the cardinality of nearly orthogonal function classes

Lee Ad Gottlieb, Aryeh Kontorovich, Elchanan Mossel

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We bound the number of nearly orthogonal vectors with fixed VC-dimension over {-1,1} n. Our bounds are of interest in machine learning and empirical process theory and improve previous bounds by Haussler. The bounds are based on a simple projection argument and they generalize to other product spaces. Along the way we derive tight bounds on the sum of binomial coefficients in terms of the entropy function.

Original languageEnglish
Pages (from-to)1766-1775
Number of pages10
JournalDiscrete Mathematics
Volume312
Issue number10
DOIs
StatePublished - 28 May 2012

Keywords

  • Orthogonal
  • Packing number
  • VC dimension

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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