Split-and-augmented Gibbs sampler - Application to large-scale inference problems

Vono, Maxime; Dobigeon, Nicolas; Chainais, Pierre

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1109/TSP.2019.2894825

Title :

Split-and-augmented Gibbs sampler - Application to large-scale inference problems

Author(s) :

Vono, Maxime [Auteur]
Signal et Communications [IRIT-SC]
Dobigeon, Nicolas [Auteur]
Signal et Communications [IRIT-SC]
Institut National Polytechnique (Toulouse) [Toulouse INP]
Chainais, Pierre [Auteur]

Centrale Lille
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]

Journal title :

IEEE Transactions on Signal Processing

Pages :

1648-1661

Publisher :

Institute of Electrical and Electronics Engineers

Publication date :

2019-03-15

ISSN :

1053-587X

HAL domain(s) :

Statistiques [stat]/Méthodologie [stat.ME]

English abstract : [en]

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the ...
Show more >This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction method of multipliers (ADMM) main steps. The proposed framework enables to derive faster and more efficient sampling schemes than the current state-of-the-art methods and can embed the latter. By sampling efficiently the parameter to infer as well as the hyperparameters of the problem, the generated samples can be used to approximate Bayesian estimators of the parameters to infer. Additionally, the proposed approach brings confidence intervals at a low cost contrary to optimization methods. Simulations on two often-studied signal processing problems illustrate the performance of the two proposed samplers. All results are compared to those obtained by recent state-of-the-art optimization and MCMC algorithms used to solve these problems. Index Terms Bayesian inference, data augmentation, high-dimensional problems, Markov chain Monte Carlo, variable splitting.Show less >

Language :

Anglais

Popular science :

Non

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