Proximal Approximate Inference in State-Space Models

• URL: http://arxiv.org/abs/2511.15409v1
• Date: Wed, 19 Nov 2025 13:06:08 GMT
• Title: Proximal Approximate Inference in State-Space Models
• Authors: Hany Abdulsamad, Ángel F. García-Fernández, Simo Särkkä,
• Abstract summary: We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models.<n>Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates.
• Score: 11.340424368313606
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

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