Denotational semantics of languages for inference: semirings, monads, and tensor...
summary
Claims an explicit algebraic route: modules over a semiring R yield monads T_R sending X to finitely supported unnormalized measures R^X and submonads fixing total mass in S, and for many probabilistic examples (nonnegative reals, polynomial ring for unknown coin bias, noncommutative state semirings) the tensor of those monads coincides with the monad for the semiring tensor. The talk gives concrete constructions, several isomorphism proofs, worked examples and counterexamples, and states sufficient-conditions work in progress.
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