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A note on bounds for VC dimensions

Aad van der Vaart, Jon A. Wellner
Source: Christian Houdré, Vladimir Koltchinskii, David M. Mason and Magda Peligrad, eds., High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2009), 103-107.

Abstract

We provide bounds for the VC dimension of class of sets formed by unions, intersections, and products of VC classes of sets $\mathcal{C}$1, …, $\mathcal{C}$m.

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Primary Subjects: 60B99
Secondary Subjects: 62G30
Keywords: Vapnik-Chervonenkis class; combining classes; inequality; entropy
Full-text: Open access
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.imsc/1265119264
Digital Object Identifier: doi:10.1214/09-IMSCOLL508

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Institute of Mathematical Statistics Collections

Institute of Mathematical Statistics Collections