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
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AN - SCOPUS:39449132151
SN - 0166-218X
VL - 156
SP - 903
EP - 910
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
IS - 6
ER -