Online Bayesian system identification in multivariate autoregressive models via message passing

TL;DR

This paper introduces a recursive Bayesian method using message passing for multivariate autoregressive models, providing full uncertainty quantification and online model evidence, outperforming traditional methods in accuracy and convergence.

Contribution

It presents a novel message passing-based Bayesian approach for online system identification that yields full posterior distributions, unlike existing methods.

Findings

Empirically converges on synthetic data

Achieves competitive results on a physical system

Provides full uncertainty quantification

Abstract

We propose a recursive Bayesian estimation procedure for multivariate autoregressive models with exogenous inputs based on message passing in a factor graph. Unlike recursive least-squares, our method produces full posterior distributions for both the autoregressive coefficients and noise precision. The uncertainties regarding these estimates propagate into the uncertainties on predictions for future system outputs, and support online model evidence calculations. We demonstrate convergence empirically on a synthetic autoregressive system and competitive performance on a double mass-spring-damper system.