VC bounds on the cardinality of nearly orthogonal function classes

Details VC bounds on the cardinality of nearly orthogonal function classes VC bounds on the cardinality of nearly orthogonal function classes

2010-07-28

arxiv.org/abs/1007.4915v2

Mathematics

Combinatorics

17 pages

Scientific paper

We bound the number of nearly orthogonal vectors with fixed VC-dimension over $\setpm^n$. 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 the generalize to other product spaces. Along the way we derive tight bounds on the sum of binomial coefficients in terms of the entropy function.

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