Statistics seminar

Abstract: In this talk, we discuss the variational inference problem in partially observed Markov processes from the dynamic programming perspective. This leads to a backward and a forward recursion for certain value functionals, which are closely connected to the corresponding recursions from classical Bayesian state estimation theory. Namely, the backward value functional is a lower bound on the "backward filter" and the forward value functional is a lower bound on the unnormalized filtering density. The two recursions can also be combined yielding a variational two-filter formula. What results is a variational state estimation theory that is completely analogous to the classical Bayesian state estimation theory. The theory is applied to a jump Gauss-Markov regression problem, where closed form solutions to the value functional recursions can be obtained.