The VC dimension of k-uniform random hypergraphs

B. Ycart, J. Ratsaby

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

A set of vertices is shattered in a hypergraph if any of its subsets is obtained as the intersection of an edge with the set. The VC dimension is the size of the largest shattered subset. Under the binomial model of k-uniform random hypergraphs, the threshold function for the VC dimension to be larger than a given integer is obtained. The same is done for the testing dimension, which is the largest integer d such that all sets of cardinality d are shattered.

Original languageEnglish
Pages (from-to)564-572
Number of pages9
JournalRandom Structures and Algorithms
Volume30
Issue number4
DOIs
StatePublished - 1 Jul 2007

Keywords

  • Random hypergraph
  • Testing dimension
  • Threshold
  • Vapnik-Chervonenkis

ASJC Scopus subject areas

  • Software
  • Mathematics (all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

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