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Register a new userBounds on the cardinality of partition
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Authors
Kerry M. Soileau
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If A is infinite and well-ordered, then |2^A|<=|Part(A)|<=|A^A|.
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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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