Optimal Learning from the Doob-Dynkin lemma

01/03/2018

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by   Gunnar Taraldsen, et al.

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The Doob-Dynkin Lemma gives conditions on two functions X and Y that ensure existence of a function ϕ so that X = ϕ∘ Y. This communication proves different versions of the Doob-Dynkin Lemma, and shows how it is related to optimal statistical learning algorithms. Keywords and phrases: Improper prior, Descriptive set theory, Conditional Monte Carlo, Fiducial, Machine learning, Complex data.