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

TL;DR

This paper introduces two new optimization-driven Monte Carlo algorithms inspired by variable splitting and data augmentation, offering faster, more efficient sampling for large-scale Bayesian inference with confidence intervals.

Contribution

The paper presents novel Monte Carlo algorithms based on variable splitting and data augmentation, closely related to ADMM, improving sampling efficiency over existing methods.

Findings

Faster convergence compared to state-of-the-art methods

Efficient sampling of parameters and hyperparameters

Provides confidence intervals at low computational cost

Abstract

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.