References & Citations
Mathematics > Statistics Theory
Title: Comparing Scale Parameter Estimators for Gaussian Process Interpolation with the Brownian Motion Prior: Leave-One-Out Cross Validation and Maximum Likelihood
(Submitted on 14 Jul 2023 (v1), last revised 17 Apr 2024 (this version, v2))
Abstract: Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation, offering a principled way of quantifying the uncertainties of predicted function values. For the quantified uncertainties to be well-calibrated, however, the kernel of the GP prior has to be carefully selected. In this paper, we theoretically compare two methods for choosing the kernel in GP regression: cross-validation and maximum likelihood estimation. Focusing on the scale-parameter estimation of a Brownian motion kernel in the noiseless setting, we prove that cross-validation can yield asymptotically well-calibrated credible intervals for a broader class of ground-truth functions than maximum likelihood estimation, suggesting an advantage of the former over the latter. Finally, motivated by the findings, we propose interior cross validation, a procedure that adapts to an even broader class of ground-truth functions.
Submission history
From: Masha Naslidnyk [view email][v1] Fri, 14 Jul 2023 16:48:34 GMT (1154kb,D)
[v2] Wed, 17 Apr 2024 19:48:28 GMT (1173kb,D)
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