Efficient Sampling through Variable Splitting-inspired Bayesian Hierarchical Models

Abstract

Markov chain Monte Carlo (MCMC) methods are an important class of computation techniques to solve Bayesian inference problems. Much recent research has been dedicated to scale these algorithms in high-dimensional settings by relying on powerful optimization tools such as gradient information or proximity operators. In a similar vein, this paper proposes a new Bayesian hierarchical model to solve large scale inference problems by taking inspiration from variable splitting methods. Similarly to the latter, the derived Gibbs sampler permits to divide the initial sampling task into simpler ones. As a result, the proposed Bayesian framework can lead to a faster sampling scheme than state-of-the-art methods by embedding them. The strength of the proposed methodology is illustrated on two often-studied image processing problems.