Moderate deviations inequalities for Gaussian process regression
Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP reg...
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| Published in | Journal of applied probability Vol. 61; no. 1; pp. 172 - 197 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.03.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0021-9002 1475-6072 |
| DOI | 10.1017/jpr.2023.30 |
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| Abstract | Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP regression. Two specific examples of broad interest are the probability of falsely ordering pairs of points (incorrectly estimating one point as being better than another) and the tail probability of the estimation error at an arbitrary point. Our inequalities connect these probabilities to the mesh norm, which measures how well the design points fill the space. |
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| AbstractList | Gaussian process regression is widely used to model an unknown function on a continuous domain by interpolating a discrete set of observed design points. We develop a theoretical framework for proving new moderate deviations inequalities on different types of error probabilities that arise in GP regression. Two specific examples of broad interest are the probability of falsely ordering pairs of points (incorrectly estimating one point as being better than another) and the tail probability of the estimation error at an arbitrary point. Our inequalities connect these probabilities to the mesh norm, which measures how well the design points fill the space. |
| Author | Ryzhov, Ilya O. Li, Jialin |
| Author_xml | – sequence: 1 givenname: Jialin surname: Li fullname: Li, Jialin email: jln.li@rotman.utoronto.ca organization: University of Toronto – sequence: 2 givenname: Ilya O. orcidid: 0000-0002-4191-084X surname: Ryzhov fullname: Ryzhov, Ilya O. email: iryzhov@rhsmith.umd.edu organization: University of Maryland |
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| Cites_doi | 10.1090/S0002-9947-01-02852-5 10.1214/009117905000000378 10.1109/TIT.2011.2182033 10.1214/17-AAP1373 10.1007/s10463-005-0017-5 10.1017/CBO9780511617539 10.1093/imanum/13.1.13 10.1080/01621459.2019.1598868 10.1016/j.jspi.2010.04.018 10.1214/009053606000000795 10.3150/14-BEJ688 10.1007/s11134-019-09632-z 10.1093/biomet/asv002 10.1287/opre.1090.0754 10.1023/A:1008306431147 10.1287/stsy.2022.0096 10.1016/0378-3758(90)90122-B 10.1214/aoap/1019737664 10.1017/jpr.2019.15 10.1109/JBHI.2014.2372777 10.1111/mice.12630 10.1007/s11222-011-9242-3 10.1137/19M1284816 10.1109/WSC.2004.1371364 10.3150/18-BEJ1074 10.1214/aop/1176992269 |
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| Copyright | The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust |
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| DOI | 10.1017/jpr.2023.30 |
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| Keywords | Gaussian process regression interpolation theory moderate deviations 60G15 62K99 |
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| SubjectTerms | Approximation Continuity (mathematics) Design of experiments Deviation Estimation Finite element method Gaussian process Inequalities Machine learning Original Article Probability Random variables Regression Statistical analysis |
| Title | Moderate deviations inequalities for Gaussian process regression |
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