Naslidnyk, Masha; Kanagawa, Motonobu; Karvonen, Toni; Mahsereci, Maren; (2025) Comparing Scale Parameter Estimators for Gaussian Process Interpolation with the Brownian Motion Prior: Leave-One-Out Cross Validation and Maximum Likelihood. SIAM/ASA Journal on Uncertainty Quantification , 13 (2) pp. 679-717. 10.1137/23m1586884.

Preview

Text 2307.07466v2.pdf - Accepted Version Download (2MB) | Preview

Abstract

Gaussian process (GP) regression is a Bayesian nonparametric method for regression and interpolation that offers 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 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.

Download activity - last month

Export as JSONCSVXML

Download activity - last 12 months

Export as XMLCSVJSON

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item