MCMC for Variationally Sparse Gaussian Processes

Part of Advances in Neural Information Processing Systems 28 (NIPS 2015)

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James Hensman, Alexander G. Matthews, Maurizio Filippone, Zoubin Ghahramani


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 sup- port 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.