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

TL;DR

This paper analyzes the accuracy of pointwise uncertainty estimates in sparse variational Gaussian process regression with a Brownian motion prior, providing theoretical guarantees and practical insights.

Contribution

It offers the first theoretical characterization of the frequentist coverage and limitations of credible sets in this specific Gaussian process framework.

Findings

Credible sets are asymptotically correct with enough inducing variables.

Identifies conditions under which credible sets are conservative or overconfident.

Provides numerical validation and discusses connections with other Gaussian process priors.

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.