Bayesian compressed sensing: Improving inference

In this paper we present a set of theoretical results regarding inference algorithms for hierarchical Bayesian networks. More specifically we focus on a specific type of networks which result in highly sparse models for the input. Bayesian inference in these networks usually is based on optimising a non-convex cost function of the model parameters. We extend previous work done in this field by providing some global performance guarantees regarding this cost function. This is the starting point for redesigning the aforementioned algorithms by employing results from well known sparse reconstruction techniques. This contribution comes in the form of three theorems. The end result is a new view of the Bayesian sparse reconstruction problem.