MCMC for variationally sparse Gaussian processes

Hensman, James and De Matthews, Alexander G. and Filippone, Maurizio and Ghahramani, Zoubin (2015) MCMC for variationally sparse Gaussian processes. In: Advances in Neural Information Processing Systems :. Neural information processing systems foundation, CAN, pp. 1648-1656.

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 is available at github.com/sparseMCMC.