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.
Keywords
VC dimension, packing number, orthogonal
Recommended Citation
Gottlieb, L., Kontorovich, A., & Mossel, E. (2012). VC Bounds on the Cardinality of Nearly Orthogonal Function Classes. Discrete Mathematics, 312 (10), 1766-1775. http://dx.doi.org/10.1016/j.disc.2012.01.030
Date Posted: 27 November 2017
This document has been peer reviewed.
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.