ONLINE VARIATIONAL MESSAGE PASSING IN THE HIERARCHICAL GAUSSIAN FILTER

We address the problem of online state and parameter estimation in hierarchical Bayesian nonlinear dynamic systems. We focus on the Hierarchical Gaussian Filter (HGF), which is a popular model in the computational neuroscience literature. For this filter, explicit equations for online state estimation (and offline parameter estimation) have been derived before. We extend this work by casting the HGF as a probabilistic factor graph and present variational message passing update rules that facilitate both online state and parameter estimation as well as online tracking of the free energy (or ELBO), which can be used as a proxy for Bayesian evidence. Due to the locality and modularity of the factor graph framework, our approach supports application of HGF's and variations as plug-in modules to a wide variety of dynamic modelling applications.