Orthogonal parallel MCMC methods for sampling and optimization

Abstract

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called {\it orthogonal MCMC} (O-MCMC), where a set of "vertical" parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters.

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Cited by in corpus (13)

• A Survey of Monte Carlo Methods for Parameter Estimation
• Physics-Aware Gaussian Processes in Remote Sensing
• A Review of Multiple Try MCMC algorithms for Signal Processing
• Group Importance Sampling for Particle Filtering and MCMC
• Active emulation of computer codes with Gaussian processes -- Application to remote sensing
• Emulation as an Accurate Alternative to Interpolation in Sampling Radiative Transfer Codes
• Metropolis Sampling
• Issues in the Multiple Try Metropolis mixing
• Parallel Metropolis chains with cooperative adaptation
• Target-aware Bayesian inference via generalized thermodynamic integration
• Accelerating MCMC Algorithms
• MCMC for a hyperbolic Bayesian inverse problem in traffic flow modelling
• Beyond Application End-Point Results: Quantifying Statistical Robustness of MCMC Accelerators