Symmetry exploits for Bayesian cubature methods

Toni Karvonen*, Simo Särkkä, Chris J. Oates

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
38 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)1231–1248
Number of pages18
JournalSTATISTICS AND COMPUTING
Volume29
Issue number6
DOIs
Publication statusPublished - 1 Jan 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Fully symmetric sets
  • Gaussian processes
  • Numerical integration
  • Probabilistic numerics

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