Variational message passing for online polynomial NARMAX identification
This addresses the problem of efficient online system identification for practitioners in control or signal processing, though it is incremental as it applies a known method to a specific model class.
The paper tackles online nonlinear system identification by proposing a variational Bayesian inference procedure for polynomial NARMAX models, showing empirically that it outperforms an online recursive least-squares estimator in small sample sizes and low noise regimes and performs on par with an offline iterative least-squares estimator.
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.