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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 empiricalprocess theory and improve previous bounds by Haussler. The bounds are based ona simple projection argument and the generalize to other product spaces. Alongthe way we derive tight bounds on the sum of binomial coefficients in terms ofthe entropy function.

VC bounds on the cardinality of nearly orthogonal function classes