Efficient Sampling through Variable Splitting-inspired Bayesian Hierarchical Models

Maxime Vono (1) , Nicolas Dobigeon (1, 2) , Pierre Chainais (3, 4)

1 IRIT-SC - Signal et Communications
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 Centrale Lille
4 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

Markov chain Monte Carlo (MCMC) methods are an important class of computation techniques to solve Bayesian inference problems. Much 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. Index Terms-Bayesian inference, Gibbs sampler, high dimension , variable splitting.

Mots clés: Gibbs sampler high dimension; Variable splitting; Bayesian inference

Domaines: Traitement du signal et de l'image [eess.SP]

Maxime Vono, Nicolas Dobigeon, Pierre Chainais. Efficient Sampling through Variable Splitting-inspired Bayesian Hierarchical Models. ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Institute of Electrical and Electronics Engineers (IEEE), May 2019, Brighton, United Kingdom. pp.5037-5041, ⟨10.1109/ICASSP.2019.8682982⟩. ⟨hal-02438055⟩