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Register a new userMetric Entropy estimation using o-minimality Theory
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Added by
Adolfo Quiroz
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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It is shown how tools from the area of Model Theory, specifically from the Theory of o-minimality, can be used to prove that a class of functions is VC-subgraph (in the sense of Dudley, 1987), and therefore satisfies a uniform polynomial metric entropy bound. We give examples where the use of these methods significantly improves the existing metric entropy bounds. The methods proposed here can be applied to finite dimensional parametric families of functions without the need for the parameters to live in a compact set, as is sometimes required in theorems that produce similar entropy bounds (for instance Theorem 19.7 of van der Vaart, 1998).
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