Symmetry exploits for Bayesian cubature methods
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2019-01-01
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Language
en
Pages
18
1231–1248
1231–1248
Series
STATISTICS AND COMPUTING, Volume 29, issue 6
Abstract
Bayesian cubature provides a flexible framework for numerical integration, in which a priori knowledge on the integrand can be encoded and exploited. This additional flexibility, compared to many classical cubature methods, comes at a computational cost which is cubic in the number of evaluations of the integrand. It has been recently observed that fully symmetric point sets can be exploited in order to reduce—in some cases substantially—the computational cost of the standard Bayesian cubature method. This work identifies several additional symmetry exploits within the Bayesian cubature framework. In particular, we go beyond earlier work in considering non-symmetric measures and, in addition to the standard Bayesian cubature method, present exploits for the Bayes–Sard cubature method and the multi-output Bayesian cubature method.Description
Keywords
Fully symmetric sets, Gaussian processes, Numerical integration, Probabilistic numerics
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Citation
Karvonen, T, Särkkä, S & Oates, C J 2019, ' Symmetry exploits for Bayesian cubature methods ', STATISTICS AND COMPUTING, vol. 29, no. 6, pp. 1231–1248 . https://doi.org/10.1007/s11222-019-09896-8