Abstract
AbstractWe define a new type of “shatter function” for set systems that satisfies a Sauer–Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah’s two-rank instead of VC dimension. We identify the least exponent bounding the rate of growth of the shatter function, the quantity analogous to VC density, with Shelah’s
$\omega $
-rank.
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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1. Model theory and agnostic online learning via excellent sets;Transactions of the American Mathematical Society;2024-09-03