Optimal Learning from the Doob-Dynkin lemma

الأصل · EN

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.