Online Bayesian system identification in multivariate autoregressive models via message passing

2025-06-03

AI Summary

This paper addresses online Bayesian system identification for multivariate autoregressive exogenous (ARX) models. We propose a recursive Bayesian inference framework based on factor graphs and variational message passing. To the best of our knowledge, this is the first method enabling exact online estimation of the full posterior distributions over both autoregressive coefficients and noise precision in ARX models, while simultaneously computing the model evidence—enabling predictive uncertainty propagation and real-time model selection. Unlike conventional recursive least squares, which yields only point estimates, our approach delivers well-calibrated probabilistic outputs. We empirically verify posterior convergence on synthetic systems and demonstrate identification accuracy comparable to state-of-the-art methods on the benchmark two-mass-spring-damper system, with highly calibrated predictive uncertainties.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Recursive Bayesian estimation for multivariate autoregressive models
• Full posterior distributions for coefficients and noise precision
• Online uncertainty propagation and model evidence calculation

Innovation

• Recursive Bayesian estimation via message passing
• Full posterior distributions for coefficients and noise
• Online model evidence calculations supported