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

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arxiv 1412.6612 v3 pith:UN4BK5KL submitted 2014-12-20 math.CO math.MGstat.ML

Christian J. J. Despres This is my paper · ORCID
classification math.COmath.MGstat.ML
keywords dimensioncubesmathbbvapnik-chervonenkiscollectioncombinatorialconceptdimensional
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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 $\lfloor(3d+1)/2\rfloor$.

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  1. VC-dimension of generalized progressions in some nonabelian groups

    math.GR 2025-05 conditional novelty 8.0 of 10

    Generalized progressions in the integer Heisenberg group have VC-dimension at most 267, and in the free group on k generators at most 3k-1.

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