Randomized Maximum Likelihood via High-Dimensional Bayesian Optimization

TL;DR

This paper introduces a high-dimensional Bayesian Optimization method using Gaussian Processes to efficiently perform Randomized Maximum Likelihood sampling in complex inverse problems, improving upon existing optimization techniques.

Contribution

It develops a novel high-dimensional Bayesian Optimization framework for RML, enhancing sampling efficiency in Bayesian inverse problems.

Findings

Outperforms alternative optimization methods on synthetic problems

Effective in real-world applications like medical imaging and magnetohydrodynamics

Demonstrates improved sampling accuracy and computational efficiency

Abstract

Posterior sampling for high-dimensional Bayesian inverse problems is a common challenge in real-world applications. Randomized Maximum Likelihood (RML) is an optimization based methodology that gives samples from an approximation to the posterior distribution. We develop a high-dimensional Bayesian Optimization (BO) approach based on Gaussian Process (GP) surrogate models to solve the RML problem. We demonstrate the benefits of our approach in comparison to alternative optimization methods on a variety of synthetic and real-world Bayesian inverse problems, including medical and magnetohydrodynamics applications.