TY - JOUR

T1 - On the complexity of constrained VC-classes

AU - Ratsaby, Joel

N1 - Funding Information:
Part of this work was done at and partially supported by the Paul Ivanier Center for Robotics Research and Production Management, Ben-Gurion University of the Negev.

PY - 2008/3/15

Y1 - 2008/3/15

N2 - Sauer's lemma is extended to classes HN 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 μh (x) of h at x ∈ [n] is defined as the largest non-negative integer a such that h is constant on the interval Ia (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].

AB - Sauer's lemma is extended to classes HN 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 μh (x) of h at x ∈ [n] is defined as the largest non-negative integer a such that h is constant on the interval Ia (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].

KW - Boolean functions

KW - Integer partitions

KW - Sauer's lemma

KW - VC-dimension

UR - http://www.scopus.com/inward/record.url?scp=39449132151&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2007.05.041

DO - 10.1016/j.dam.2007.05.041

M3 - Article

AN - SCOPUS:39449132151

VL - 156

SP - 903

EP - 910

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 6

ER -