A Constrained version of Sauer’s Lemma
نویسنده
چکیده
Sauer’s Lemma is extended to classes H of binary-valued functions on [n] = {1, . . . , n} which have a margin less than or equal to N on x ∈ [n], where the margin μh(x) of a binary valued function h at a point x ∈ [n] is defined as the largest nonnegative integer a such that h is constant on the interval Ia(x) = [x−a, x+a] ⊆ [n]. Estimates are obtained for the cardinality of classes of binary valued functions with a margin of at least N on a sample S ⊆ [n].
منابع مشابه
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تاریخ انتشار 2004