[Exclusive] ICML 2020 Best Paper Award Honorable Mention: Efficiently Sampling Functions from Gaussian Process Posteriors - CrossMinds.ai
[Exclusive] ICML 2020 Best Paper Award Honorable Mention: Efficiently Sampling Functions from Gaussian Process Posteriors
Jul 23, 202080 views
CrossMinds Editorial Team
Full Paper: https://arxiv.org/pdf/2002.09309.pdf

Authors: James T. Wilson, Viacheslav Borovitskiy, Alexander Terenin, Peter Mostowsky, and Marc Peter Deisenroth 

Abstract:
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.
ICML 2020
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