On the complexity of constrained VC-classes

Joel Ratsaby

doi:10.1016/j.dam.2007.05.041

On the complexity of constrained VC-classes

Joel Ratsaby

Research output: Contribution to journal › Article › peer-review

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 μ_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].

Original language	English
Pages (from-to)	903-910
Number of pages	8
Journal	Discrete Applied Mathematics
Volume	156
Issue number	6
DOIs	https://doi.org/10.1016/j.dam.2007.05.041
State	Published - 15 Mar 2008
Externally published	Yes

Keywords

Boolean functions
Integer partitions
Sauer's lemma
VC-dimension

Access to Document

10.1016/j.dam.2007.05.041

Cite this

@article{350b8c0127ad4aab8d4da952e49247fa,

title = "On the complexity of constrained VC-classes",

abstract = "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].",

keywords = "Boolean functions, Integer partitions, Sauer's lemma, VC-dimension",

author = "Joel Ratsaby",

note = "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. ",

year = "2008",

month = mar,

day = "15",

doi = "10.1016/j.dam.2007.05.041",

language = "אנגלית",

volume = "156",

pages = "903--910",

journal = "Discrete Applied Mathematics",

issn = "0166-218X",

publisher = "Elsevier B.V.",

number = "6",

}

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 - https://www.scopus.com/pages/publications/39449132151

U2 - 10.1016/j.dam.2007.05.041

DO - 10.1016/j.dam.2007.05.041

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:39449132151

SN - 0166-218X

VL - 156

SP - 903

EP - 910

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 6

ER -

On the complexity of constrained VC-classes

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this