On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach

TL;DR

This paper introduces a pseudo-marginal MCMC approach for variationally sparse Gaussian processes, enabling scalable and exact inference on large datasets with complex models, improving computational efficiency and flexibility.

Contribution

It proposes a novel pseudo-marginal scheme that addresses intractable likelihood evaluations in variationally sparse GPs, enhancing scalability and accuracy in complex models.

Findings

Demonstrates asymptotically exact inference with the proposed method

Achieves computational gains through doubly stochastic estimators

Effectively models non-stationarity in GP regression

Abstract

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden, approximation of the posterior, choice of the covariance function and inference of its hyperparmeters. To address these issues, Hensman et al. (2015) combine variationally sparse GPs with Markov chain Monte Carlo (MCMC) to derive a scalable, flexible and general framework for GP models. Nevertheless, the resulting approach requires intractable likelihood evaluations for many observation models. To bypass this problem, we propose a pseudo-marginal (PM) scheme that offers asymptotically exact inference as well as computational gains through doubly stochastic estimators for the intractable likelihood and large datasets. In complex models, the advantages of the PM scheme are particularly evident, and we demonstrate this on a two-level GP regression model with a nonparametric covariance function to capture non-stationarity.