Variational inference via measure transport: algorithms for Bayesian filtering and smoothing

We describe a nonparametric variational inference method that approximates an intractable target measure as the pushforward of a tractable distribution (e.g., a Gaussian) through a transport map, and that can approximate arbitrary probabilistic interactions, well beyond the usual mean-field approximations. We then show how such transport maps can be decomposed---i.e., factorized into the composition of finitely many low-dimensional maps---and establish a connection between decomposable transport maps and the sparsification of Markov networks. Finally, we use the notion of decomposable transports to derive new deterministic online algorithms for Bayesian filtering and smoothing in nonlinear/non-Gaussian state-space models with static parameters. 

This is a joint work with Daniele Bigoni and Youssef Marzouk.