The Vapnik-Chervonenkis dimension of cubes in $\mathbb{R}^d$

Christian J. J. Despres

The Vapnik-Chervonenkis dimension of cubes in $\mathbb{R}^d$

Combinatorics 2017-11-28 v3 Metric Geometry Machine Learning

Authors: Christian J. J. Despres

Abstract

The Vapnik-Chervonenkis (VC) dimension of a collection of subsets of a set is an important combinatorial concept in settings such as discrete geometry and machine learning. In this paper we prove that the VC dimension of the family of $d$ -dimensional cubes in $\mathbb R^d$ is $\lfloor(3d+1)/2\rfloor$ .

Keywords

vapnik-chervonenkis dimension cubes discrete geometry combinatorics vc dimension hypercube

Cite

@article{arxiv.1412.6612,
  title  = {The Vapnik-Chervonenkis dimension of cubes in $\mathbb{R}^d$},
  author = {Christian J. J. Despres},
  journal= {arXiv preprint arXiv:1412.6612},
  year   = {2017}
}

Comments

Derived from Fall 2014 Honours research project done under the supervision of Dr. Vladimir Pestov at the University of Ottawa; 4 pages; significantly simplified the constructions, removed the final two sections (which did not fit well with the rest)

The Vapnik-Chervonenkis dimension of cubes in $\mathbb{R}^d$

Abstract

Keywords

Cite

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