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

Published 20 Dec 2014 in math.CO, math.MG, and stat.ML | (1412.6612v3)

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 $\mathbb Rd$ is $\lfloor(3d+1)/2\rfloor$.

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