Statistics Papers

Document Type

Journal Article

Date of this Version

5-28-2012

Publication Source

Discrete Mathematics

Volume

312

Issue

10

Start Page

1766

Last Page

1775

DOI

10.1016/j.disc.2012.01.030

Abstract

We bound the number of nearly orthogonal vectors with fixed VC-dimension over {−1,1}n. Our bounds are of interest in machine learning and empirical process theory and improve previous bounds by Haussler. The bounds are based on a simple projection argument and they generalize to other product spaces. Along the way we derive tight bounds on the sum of binomial coefficients in terms of the entropy function.

Copyright/Permission Statement

© 2012. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.

Comments

At the time of publication, author Elchanan Mossel was affiliated with the University of California, Berkeley. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

Keywords

VC dimension, packing number, orthogonal

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Date Posted: 27 November 2017

This document has been peer reviewed.