Recursive Entropic Variational Inference for Nonlinear State-Space Models

Hany Abdulsamad; Ángel F. García-Fernández; Simo Särkkä

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arXiv · 2511.15409

Recursive Entropic Variational Inference for Nonlinear State-Space Models

Hany Abdulsamad·Ángel F. García-Fernández·Simo Särkkä

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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 consistency 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.

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Hany Abdulsamad, Ángel F. García-Fernández, Simo Särkkä. 2025-11-19. Recursive Entropic Variational Inference for Nonlinear State-Space Models. https://arxiv.org/abs/2511.15409

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