MCMC for Variationally Sparse Gaussian Processes

TL;DR

This paper introduces a hybrid Monte Carlo method for variationally sparse Gaussian processes, enabling efficient, non-Gaussian posterior approximations for large datasets and complex likelihoods.

Contribution

It presents a novel hybrid Monte Carlo sampling scheme that combines variational sparsity with non-Gaussian posterior approximation in Gaussian processes.

Findings

Efficient computation with large datasets using inducing points.

Simultaneous non-Gaussian posterior estimation for functions and parameters.

Code availability facilitates reproducibility.

Abstract

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate covariance function parameter posteriors. This paper simultaneously addresses these, using a variational approximation to the posterior which is sparse in support of the function but otherwise free-form. The result is a Hybrid Monte-Carlo sampling scheme which allows for a non-Gaussian approximation over the function values and covariance parameters simultaneously, with efficient computations based on inducing-point sparse GPs. Code to replicate each experiment in this paper will be available shortly.