Mixture representation of the matérn class with applications in state space approximations and Bayesian quadrature

Filip Tronarp, Toni Karvonen, Simo Särkkä

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Abstract

In this paper, the connection between the Matérn kernel and scale mixtures of squared exponential kernels is explored. It is shown that the Matérn kernel can be approximated by a finite scale mixture of squared exponential kernels through a quadrature approximation which in turn allows for (i) state space approximations of the Matérn kernel for arbitrary smoothness parameters using established state space approximations of the squared exponential kernel and (ii) exact calculation of the Bayesian quadrature weights for the approximate kernel under a Gaussian measure. The method is demonstrated in inference in a log-Gaussian Cox process as well as in approximating a Gaussian integral arising from a financial problem using Bayesian quadrature.

Original languageEnglish
Title of host publicationProceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018
EditorsNelly Pustelnik, Zheng-Hua Tan, Zhanyu Ma, Jan Larsen
Number of pages6
Volume2018-September
ISBN (Electronic)9781538654774
DOIs
Publication statusPublished - 31 Oct 2018
MoE publication typeA4 Article in a conference publication
EventIEEE International Workshop on Machine Learning for Signal Processing - Aalborg, Denmark
Duration: 17 Sep 201820 Sep 2018
Conference number: 28

Publication series

NameIEEE International Workshop on Machine Learning for Signal Processing
PublisherIEEE
ISSN (Print)2161-0363
ISSN (Electronic)2161-0371

Workshop

WorkshopIEEE International Workshop on Machine Learning for Signal Processing
Abbreviated titleMLSP
CountryDenmark
CityAalborg
Period17/09/201820/09/2018

Keywords

  • Bayesian quadrature
  • Gaussian process regression
  • Matérn covariance
  • Scale mixture representation
  • State space approximation

Projects

Sequential Monte Carlo Methods for State and Parameter Estimation in Stochastic Dynamic Systems

Särkkä, S.

01/06/201531/08/2018

Project: Academy of Finland: Other research funding

Cite this

Tronarp, F., Karvonen, T., & Särkkä, S. (2018). Mixture representation of the matérn class with applications in state space approximations and Bayesian quadrature. In N. Pustelnik, Z-H. Tan, Z. Ma, & J. Larsen (Eds.), Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018 (Vol. 2018-September). [8516992] (IEEE International Workshop on Machine Learning for Signal Processing). https://doi.org/10.1109/MLSP.2018.8516992