Variational message passing for online polynomial NARMAX identification

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...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Kouw, Wouter, Podusenko, Albert, Koudahl, Magnus, Schoukens, Maarten
Format: Article
Language:English
Subjects:
Algorithms
Bayesian analysis
Iterative methods
Least squares
Low noise
Message passing
Nonlinear systems
Parameter identification
Polynomials
Statistical inference
System identification
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Summary: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.
ISSN:2331-8422