Bayesian quadrature for multiple related integrals

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Title: Bayesian quadrature for multiple related integrals
Authors: Xi, X
Briol, F-X
Girolami, M
Item Type: Conference Paper
Abstract: Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to incomplete/finite information about the continuous mathematical problem being approximated. In this paper, we demonstrate that this paradigm can provide additional advantages, such as the possibility of transferring information between several numerical methods. This allows users to represent uncertainty in a more faithful manner and, as a by-product, provide increased numerical efficiency. We propose the first such numerical method by extending the well-known Bayesian quadrature algorithm to the case where we are interested in computing the integral of several related functions. We then prove convergence rates for the method in the well-specified and misspecified cases, and demonstrate its efficiency in the context of multi-fidelity models for complex engineering systems and a problem of global illumination in computer graphics.
Issue Date: 10-Jul-2018
Date of Acceptance: 11-May-2018
URI: http://hdl.handle.net/10044/1/65979
ISSN: 2640-3498
Publisher: PMLR
Start Page: 5373
End Page: 5382
Journal / Book Title: Proceedings of Macine Learning Research
Volume: 80
Copyright Statement: © 2018 by the author(s)
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/R018413/1
EP/K034154/1
Conference Name: 35th International Conference on Machine Learning 2018
Keywords: stat.CO
cs.NA
math.NA
stat.ML
Notes: Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:5369-5378, 2018
Publication Status: Published
Start Date: 2018-07-10
Finish Date: 2018-07-15
Conference Place: Stockholm, Sweden
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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