A Bayes–Sard Cubature Method

Toni Karvonen, Chris J. Oates, Simo Särkkä

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference contributionScientificvertaisarvioitu

Abstrakti

This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes–Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are well-established. This is achieved by considering a Gaussian process model for the integrand whose mean is a parametric regression model, with an improper prior on each regression coefficient. The features in the regression model consist of test functions which are guaranteed to be exactly integrated, with remaining degrees of freedom afforded to the non-parametric part. The asymptotic convergence of the Bayes–Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.
AlkuperäiskieliEnglanti
OtsikkoAdvances in Neural Information Processing Systems 31
AlaotsikkoProceedings of NIPS2017
KustantajaCurran Associates, Inc.
Sivumäärä12
TilaJulkaistu - joulukuuta 2018
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisuussa
TapahtumaConference on Neural Information Processing Systems - Palais des Congrès de Montréal, Montréal, Kanada
Kesto: 2 joulukuuta 20188 joulukuuta 2018
Konferenssinumero: 32
http://nips.cc

Julkaisusarja

NimiAdvances in neural information processing systems
KustantajaCurran Associates
Numero31
ISSN (painettu)1049-5258

Conference

ConferenceConference on Neural Information Processing Systems
LyhennettäNeurIPS
MaaKanada
KaupunkiMontréal
Ajanjakso02/12/201808/12/2018
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