Gaussian Processes to speed up MCMC with automatic exploratory-exploitation effect

TL;DR

This paper introduces a two-stage Metropolis-Hastings algorithm utilizing Gaussian Processes to efficiently sample complex probabilistic models without pre-training, enabling automatic inference in probabilistic programming.

Contribution

It presents a novel two-stage sampling method that learns the target distribution during sampling, eliminating the need for pre-trained surrogates, and extends this to MALA.

Findings

Effective sampling with expensive likelihoods

Automatic learning of the target distribution

Extension to MALA algorithm

Abstract

We present a two-stage Metropolis-Hastings algorithm for sampling probabilistic models, whose log-likelihood is computationally expensive to evaluate, by using a surrogate Gaussian Process (GP) model. The key feature of the approach, and the difference w.r.t. previous works, is the ability to learn the target distribution from scratch (while sampling), and so without the need of pre-training the GP. This is fundamental for automatic and inference in Probabilistic Programming Languages In particular, we present an alternative first stage acceptance scheme by marginalising out the GP distributed function, which makes the acceptance ratio explicitly dependent on the variance of the GP. This approach is extended to Metropolis-Adjusted Langevin algorithm (MALA).