Fast Bayesian Estimation Using Location-Type Variational Representations

Abstract

A class of iterative Bayesian estimation methods known as Type I methods use a variational representation of the posterior distribution. However, Type I methods can exhibit slow convergence for a family of variational representations referred to as convex/location representation. We analyze the convergence behavior of Type I methods by interpreting them as an iterative maximization of a dual objective function involving a linearization. We then propose a modified method that avoids the linearization and allows a coordinatewise maximization. We demonstrate the advantages of the proposed method in the context of image restoration under Poisson noise.