Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion prior

Luke Travis, Kolyan Ray

Keywords: Gaussian process, sparse variational Bayes, uncertainty quantification, theoretical guarantees

TL;DR: We study theoretical guarantees for pointwise uncertainty quantification using a sparse variational Gaussian process method based on a Brownian motion prior.

Abstract: We study pointwise estimation and uncertainty quantification for a sparse variational Gaussian process method with eigenvector inducing variables. For a rescaled Brownian motion prior, we derive theoretical guarantees and limitations for the frequentist size and coverage of pointwise credible sets. For sufficiently many inducing variables, we precisely characterize the asymptotic frequentist coverage, deducing when credible sets from this variational method are conservative and when overconfident/misleading. We numerically illustrate the applicability of our results and discuss connections with other common Gaussian process priors.

Submission Number: 1434