The Restricted Variational Bayes Approximation in Bayesian Filtering

The Variational Bayes (VB) approach is used as a one-step approximation for Bayesian filtering. It requires the availability of moments of the free-form distributional optimizers. The latter may have intractable functional forms. In this contribution, we replace these by appropriate fixed-form distributions yielding the required moments. We address two scenarios of this Restricted VB (RVB) approximation. For the first scenario, an application in identification of HMMs is given. Close relationship of the second scenario to Rao-Blackwellized particle filtering is discussed and their performance is illustrated on a simple non-linear model.