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Mathematics > Statistics Theory
Title: Pointwise uncertainty quantification for sparse variational Gaussian process regression with a Brownian motion prior
(Submitted on 29 Sep 2023 (v1), last revised 31 Oct 2023 (this version, v3))
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 history
From: Luke Travis [view email][v1] Fri, 29 Sep 2023 19:11:47 GMT (58kb,D)
[v2] Mon, 9 Oct 2023 08:20:23 GMT (59kb,D)
[v3] Tue, 31 Oct 2023 16:54:41 GMT (68kb,D)
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