On the Vapnik-Chervonenkis dimension of products of intervals in $\mathbb{R}^d$

Autor:	Gómez, Alirio Gómez, Kaufmann, Pedro L.
Rok vydání:	2021
Předmět:	Mathematics - Metric Geometry Computer Science - Machine Learning Mathematics - Combinatorics Statistics - Machine Learning
Druh dokumentu:	Working Paper
Popis:	We study combinatorial complexity of certain classes of products of intervals in $\mathbb{R}^d$, from the point of view of Vapnik-Chervonenkis geometry. As a consequence of the obtained results, we conclude that the Vapnik-Chervonenkis dimension of the set of balls in $\ell_\infty^d$ -- which denotes $\R^d$ equipped with the sup norm -- equals $\lfloor (3d+1)/2\rfloor$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2104.07136 Zobrazit plný text záznamu View this record from Arxiv