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...

Full description

Saved in:
Bibliographic Details
Published inJournal of applied probability Vol. 61; no. 1; pp. 172 - 197
Main Authors Li, Jialin, Ryzhov, Ilya O.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.03.2024
Subjects
Approximation
Continuity (mathematics)
Design of experiments
Deviation
Estimation
Finite element method
Gaussian process
Inequalities
Machine learning
Original Article
Probability
Random variables
Regression
Statistical analysis
Gaussian process regression
interpolation theory
moderate deviations
60G15
62K99
Online AccessGet full text
ISSN0021-9002
1475-6072
DOI10.1017/jpr.2023.30

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2023.30