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

Tronarp, Filip LU ; Karvonen, Toni and Särkkä, Simo (2018)
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.
Please use this url to cite or link to this publication:
author
; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:85057002621
ISBN
978-1-5386-5477-4
978-1-5386-5478-1
DOI
10.1109/MLSP.2018.8516992
language
English
LU publication?
no
id
d84e99d6-0496-45e6-975b-0b58128305e7
date added to LUP
2023-08-20 23:02:21
date last changed
2024-06-29 07:23:36
@inproceedings{d84e99d6-0496-45e6-975b-0b58128305e7,
  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.}},
  author       = {{Tronarp, Filip and Karvonen, Toni and Särkkä, Simo}},
  booktitle    = {{IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)}},
  isbn         = {{978-1-5386-5477-4}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Mixture representation of the Matérn class with applications in state space approximations and Bayesian quadrature}},
  url          = {{http://dx.doi.org/10.1109/MLSP.2018.8516992}},
  doi          = {{10.1109/MLSP.2018.8516992}},
  year         = {{2018}},
}