Vapnik–Chervonenkis dimension of axis-parallel cuts

Servane Gey

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 9, 2291-2296

Abstract: Algorithms in high dimension uses axis-parallel cuts to partition Rd${\mathbb {R}}^d$ in order to reduce the computational time of classifiers or regressors. Evaluating the complexity of such partitions is then crucial to evaluate estimation performance. In this framework, we show that the Vapnik–Chervonenkis dimension (VC dimension) of the set of half-spaces of Rd${\mathbb {R}}^d$ with frontiers parallel to the axes is of the order of log 2d.

Date: 2018
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DOI: 10.1080/03610926.2017.1339088

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