Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions
(2020) In SIAM/ASA Journal on Uncertainty Quantification 8(3).- Abstract
- Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the data set. This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless data set. Specifically, we consider the scenario where the scale parameter of a Sobolev kernel (such as a Matérn kernel) is estimated by maximum likelihood. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become “slowly” overconfident at worst, regardless of... (More)
- Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the data set. This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless data set. Specifically, we consider the scenario where the scale parameter of a Sobolev kernel (such as a Matérn kernel) is estimated by maximum likelihood. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become “slowly” overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model. The analysis is based on a combination of techniques from nonparametric regression and scattered data interpolation. Empirical results are provided in support of the theoretical findings. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7fada72c-ed66-482c-8481-33245816e952
- author
- Tronarp, Filip LU ; Karvonen, Toni ; Wynne, George ; Oates, Chris and Särkkä, Simo
- publishing date
- 2020
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- nonparametric regression, scattered data approximation, credible sets, Bayesian cubature, model misspecification
- in
- SIAM/ASA Journal on Uncertainty Quantification
- volume
- 8
- issue
- 3
- pages
- 33 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:85093520595
- ISSN
- 2166-2525
- DOI
- 10.1137/20M1315968
- language
- English
- LU publication?
- no
- id
- 7fada72c-ed66-482c-8481-33245816e952
- date added to LUP
- 2023-08-20 22:36:39
- date last changed
- 2023-10-13 16:06:59
@article{7fada72c-ed66-482c-8481-33245816e952,
abstract = {{Despite the ubiquity of the Gaussian process regression model, few theoretical results are available that account for the fact that parameters of the covariance kernel typically need to be estimated from the data set. This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless data set. Specifically, we consider the scenario where the scale parameter of a Sobolev kernel (such as a Matérn kernel) is estimated by maximum likelihood. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model in the sense that the model can become “slowly” overconfident at worst, regardless of the difference between the smoothness of the data-generating function and that expected by the model. The analysis is based on a combination of techniques from nonparametric regression and scattered data interpolation. Empirical results are provided in support of the theoretical findings.}},
author = {{Tronarp, Filip and Karvonen, Toni and Wynne, George and Oates, Chris and Särkkä, Simo}},
issn = {{2166-2525}},
keywords = {{nonparametric regression; scattered data approximation; credible sets; Bayesian cubature; model misspecification}},
language = {{eng}},
number = {{3}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{SIAM/ASA Journal on Uncertainty Quantification}},
title = {{Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions}},
url = {{http://dx.doi.org/10.1137/20M1315968}},
doi = {{10.1137/20M1315968}},
volume = {{8}},
year = {{2020}},
}