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Title: Scalable Gaussian Process Inference with Finite-data Mean and Variance Guarantees
Gaussian processes (GPs) offer a flexible class of priors for nonparametric Bayesian regression, but popular GP posterior inference methods are typically prohibitively slow or lack desirable finite-data guarantees on quality. We develop a scalable approach to approximate GP regression, with finite-data guarantees on the accuracy of our pointwise posterior mean and variance estimates. Our main contribution is a novel objective for approximate inference in the nonparametric setting: the preconditioned Fisher (pF) divergence. We show that unlike the Kullback–Leibler divergence (used in variational inference), the pF divergence bounds bounds the 2-Wasserstein distance, which in turn provides tight bounds on the pointwise error of mean and variance estimates. We demonstrate that, for sparse GP likelihood approximations, we can minimize the pF divergence bounds efficiently. Our experiments show that optimizing the pF divergence bounds has the same computational requirements as variational sparse GPs while providing comparable empirical performance—in addition to our novel finite-data quality guarantees.  more » « less
Award ID(s):
1750286
NSF-PAR ID:
10154449
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of Machine Learning Research
ISSN:
2640-3498
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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