# Recursive Entropic Variational Inference for Nonlinear State-Space Models

arXiv: https://arxiv.org/abs/2511.15409 · HTML: https://mlsanity.com/paper/2511.15409/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 64 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 25 of 25)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Models](https://mlsanity.com/paper/1703.04265/) (2017)
- [Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective](https://mlsanity.com/paper/1810.03440/) (2018)
- [SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equations](https://mlsanity.com/paper/2502.02472/) (2025)
- [Fast Variational Learning in State-Space Gaussian Process Models](https://mlsanity.com/paper/2007.04731/) (2020)
- [Online Variational Filtering and Parameter Learning](https://mlsanity.com/paper/2110.13549/) (2021)
- [Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2110.11847/) (2021)
- [Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guarantees](https://mlsanity.com/paper/2111.01721/) (2021)
- [Variational Gaussian Process Diffusion Processes](https://mlsanity.com/paper/2306.02066/) (2023)
- [State Space Expectation Propagation: Efficient Inference Schemes for Temporal Gaussian Processes](https://mlsanity.com/paper/2007.05994/) (2020)
- [A trust-region method for stochastic variational inference with applications to streaming data](https://mlsanity.com/paper/1505.07649/) (2015)
- [Exactly Sparse Gaussian Variational Inference with Application to Derivative-Free Batch Nonlinear State Estimation](https://mlsanity.com/paper/1911.08333/) (2019)
- [Moment-Based Variational Inference for Stochastic Differential Equations](https://mlsanity.com/paper/2103.00988/) (2021)
- [Parallel square-root statistical linear regression for inference in nonlinear state space models](https://mlsanity.com/paper/2207.00426/) (2022)
- [SING: SDE Inference via Natural Gradients](https://mlsanity.com/paper/2506.17796/) (2025)
- [Gaussian Variational State Estimation for Nonlinear State-Space Models](https://mlsanity.com/paper/2002.02620/) (2020)
- [Parallel-in-Time Probabilistic Numerical ODE Solvers](https://mlsanity.com/paper/2310.01145/) (2023)
- [Fourier--Hermite Dynamic Programming for Optimal Control](https://mlsanity.com/paper/2202.13453/) (2022)
- [Damped Posterior Linearization Filter](https://mlsanity.com/paper/1704.01113/) (2017)
- [Posterior linearisation smoothing with robust iterations](https://mlsanity.com/paper/2112.03969/) (2021)
- [Variational Gaussian filtering via Wasserstein gradient flows](https://mlsanity.com/paper/2303.06398/) (2023)
- [A Recursive Theory of Variational State Estimation: The Dynamic Programming Approach](https://mlsanity.com/paper/2511.11497/) (2025)

## Abstract (arXiv)

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.