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Poster
Efficiently sampling functions from Gaussian process posteriors
James Wilson · Viacheslav Borovitskiy · Alexander Terenin · Peter Mostowsky · Marc Deisenroth

Thu Jul 16 02:00 PM -- 02:45 PM & Fri Jul 17 03:00 AM -- 03:45 AM (PDT) @
in Poster Session 47 »

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of larger frameworks, wherein quantities of interest are ultimately defined by integrating over posterior distributions. These quantities are frequently intractable, motivating the use of Monte Carlo methods. Despite substantial progress in scaling up Gaussian processes to large training sets, methods for accurately generating draws from their posterior distributions still scale cubically in the number of test locations. We identify a decomposition of Gaussian processes that naturally lends itself to scalable sampling by separating out the prior from the data. Building off of this factorization, we propose an easy-to-use and general-purpose approach for fast posterior sampling, which seamlessly pairs with sparse approximations to afford scalability both during training and at test time. In a series of experiments designed to test competing sampling schemes' statistical properties and practical ramifications, we demonstrate how decoupled sample paths accurately represent Gaussian process posteriors at a fraction of the usual cost.

Keywords: Gaussian Processes

Author Information

James Wilson (Imperial College London)
Viacheslav Borovitskiy (St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences (PDMI RAS))
Alexander Terenin (Imperial College London)
Peter Mostowsky (Saint Petersburg State University)
Marc Deisenroth (University College London)

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