# Variational message passing for online polynomial NARMAX identification

arXiv: https://arxiv.org/abs/2204.00769 · HTML: https://mlsanity.com/paper/2204.00769/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 2 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Deep Energy-Based NARX Models](https://mlsanity.com/paper/2012.04136/) (2020)
- [Sequential Monte Carlo Methods for System Identification](https://mlsanity.com/paper/1503.06058/) (2015)
- [On the Simulation of Polynomial NARMAX Models](https://mlsanity.com/paper/1810.06883/) (2018)
- [Online system identification in a Duffing oscillator by free energy minimisation](https://mlsanity.com/paper/2009.00845/) (2020)

## Built on by (most cited first, 1 of 1)

- [Information-seeking polynomial NARX model-predictive control through expected free energy minimization](https://mlsanity.com/paper/2312.15046/) (2023)

## Abstract (arXiv)

We propose a variational Bayesian inference procedure for online nonlinear system identification. For each output observation, a set of parameter posterior distributions is updated, which is then used to form a posterior predictive distribution for future outputs. We focus on the class of polynomial NARMAX models, which we cast into probabilistic form and represent in terms of a Forney-style factor graph. Inference in this graph is efficiently performed by a variational message passing algorithm. We show empirically that our variational Bayesian estimator outperforms an online recursive least-squares estimator, most notably in small sample size settings and low noise regimes, and performs on par with an iterative least-squares estimator trained offline.