@article{5b1e61af0e1a4f0284498596f5d30943,
title = "VC bounds on the cardinality of nearly orthogonal function classes",
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.",
keywords = "Orthogonal, Packing number, VC dimension",
author = "Gottlieb, {Lee Ad} and Aryeh Kontorovich and Elchanan Mossel",
note = "Funding Information: The third author was partially supported by DMS 0548249 (CAREER) award, by ISF grant 1300/08 , by a Minerva Foundation grant and by an ERC Marie Curie Grant 2008 239317 . Funding Information: The first author{\textquoteright}s work was supported in part by The Israel Science Foundation (grant #452/08 ), and by a Minerva grant. ",
year = "2012",
month = may,
day = "28",
doi = "10.1016/j.disc.2012.01.030",
language = "אנגלית",
volume = "312",
pages = "1766--1775",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "10",
}