Approximate Sampling using an Accelerated Metropolis-Hastings based on Bayesian Optimization and Gaussian Processes
This addresses efficiency issues in MCMC for unimodal distributions, particularly with big data, but is incremental as it builds on existing MH methods.
The paper tackles the problem of computationally expensive target distributions in Metropolis-Hastings MCMC by proposing an enhanced algorithm that uses Bayesian optimization and Gaussian processes to reduce function evaluations and improve proposal distributions, showing significant improvement over regular MH in experiments.
Markov Chain Monte Carlo (MCMC) methods have a drawback when working with a target distribution or likelihood function that is computationally expensive to evaluate, specially when working with big data. This paper focuses on Metropolis-Hastings (MH) algorithm for unimodal distributions. Here, an enhanced MH algorithm is proposed that requires less number of expensive function evaluations, has shorter burn-in period, and uses a better proposal distribution. The main innovations include the use of Bayesian optimization to reach the high probability region quickly, emulating the target distribution using Gaussian processes (GP), and using Laplace approximation of the GP to build a proposal distribution that captures the underlying correlation better. The experiments show significant improvement over the regular MH. Statistical comparison between the results from two algorithms is presented.