On the complexity of constrained VC-classes

Authors:
Joel Ratsaby
Affiliations:
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 5
Cited 0

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Abstract

Sauer's lemma is extended to classes H"N of binary-valued functions h on [n]={1,...,n} which have a margin less than or equal to N on all x@?[n] with h(x)=1, where the margin @m"h(x) of h at x@?[n] is defined as the largest non-negative integer a such that h is constant on the interval I"a(x)=[x-a,x+a]@?[n]. Estimates are obtained for the cardinality of classes of binary-valued functions with a margin of at least N on a positive sample S@?[n].