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VC bounds on the cardinality of nearly orthogonal function classes

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 Added by Aryeh Kontorovich
 Publication date 2010
  fields
and research's language is English




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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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