Pseudo-Marginal Bayesian Inference for Gaussian Processes

TL;DR

This paper introduces a pseudo-marginal MCMC method for Gaussian Processes that improves Bayesian inference and uncertainty quantification, enabling full Bayesian analysis and better predictive performance.

Contribution

It presents a novel pseudo-marginal approach for Gaussian Process inference that enhances sampling efficiency and uncertainty estimation over existing methods.

Findings

Improved sampling efficiency over traditional methods

Feasibility of Monte Carlo integration of all model parameters

Enhanced uncertainty quantification in predictions

Abstract

The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on out-of-sample data. Using probit regression as an illustrative working example, this paper presents a general and effective methodology based on the pseudo-marginal approach to Markov chain Monte Carlo that efficiently addresses both of these issues. The results presented in this paper show improvements over existing sampling methods to simulate from the posterior distribution over the parameters defining the covariance function of the Gaussian Process prior. This is particularly important as it offers a powerful tool to carry out full Bayesian inference of Gaussian Process based hierarchic statistical models in general. The results also demonstrate that Monte Carlo based integration of all model parameters is actually feasible in this class of models providing a superior quantification of uncertainty in predictions. Extensive comparisons with respect to state-of-the-art probabilistic classifiers confirm this assertion.