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
Issue number10
StatePublished - 28 May 2012


  • Orthogonal
  • Packing number
  • VC dimension

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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