Proximal Approximate Inference in State-Space Models

TL;DR

This paper introduces a novel variational Lagrangian approach for state estimation in complex nonlinear, non-Gaussian models, resulting in efficient recursive algorithms with broad applicability.

Contribution

It develops a new variational framework for approximate inference in state-space models, unifying trust-region updates with recursive algorithms for nonlinear, non-Gaussian cases.

Findings

Recursive schemes with low computational complexity

Effective approximation for nonlinear, non-Gaussian models

Versatile framework applicable to various models

Abstract

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic constraints. This framework gives rise to a family of forward-backward algorithms, whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.