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

Filip Tronarp; Toni Karvonen; Simo Särkkä

doi:10.1109/MLSP.2018.8516992

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

Filip Tronarp, Toni Karvonen, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

3 Citations (Scopus)

886 Downloads (Pure)

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 language	English
Title of host publication	Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018
Editors	Nelly Pustelnik, Zheng-Hua Tan, Zhanyu Ma, Jan Larsen
Publisher	IEEE
Number of pages	6
Volume	2018-September
ISBN (Electronic)	9781538654774
DOIs	https://doi.org/10.1109/MLSP.2018.8516992
Publication status	Published - 31 Oct 2018
MoE publication type	A4 Conference publication
Event	IEEE International Workshop on Machine Learning for Signal Processing - Aalborg, Denmark Duration: 17 Sept 2018 → 20 Sept 2018 Conference number: 28

Publication series

Name	IEEE International Workshop on Machine Learning for Signal Processing
Publisher	IEEE
ISSN (Print)	2161-0363
ISSN (Electronic)	2161-0371

Workshop

Workshop	IEEE International Workshop on Machine Learning for Signal Processing
Abbreviated title	MLSP
Country/Territory	Denmark
City	Aalborg
Period	17/09/2018 → 20/09/2018

Keywords

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

Access to Document

10.1109/MLSP.2018.8516992

ELEC_Tronarp_etal_Mixture-Presentation-of-the-Matern_MLSP2018Accepted author manuscript, 364 KB

OpenUrl availability

Full text

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). Article 8516992 (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP.2018.8516992

Tronarp, Filip ; Karvonen, Toni ; Särkkä, Simo. / Mixture representation of the matérn class with applications in state space approximations and Bayesian quadrature. Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018. editor / Nelly Pustelnik ; Zheng-Hua Tan ; Zhanyu Ma ; Jan Larsen. Vol. 2018-September IEEE, 2018. (IEEE International Workshop on Machine Learning for Signal Processing).

@inproceedings{e197168b40834e538383535c5aa17033,

title = "Mixture representation of the mat{\'e}rn class with applications in state space approximations and Bayesian quadrature",

abstract = "In this paper, the connection between the Mat{\'e}rn kernel and scale mixtures of squared exponential kernels is explored. It is shown that the Mat{\'e}rn 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 Mat{\'e}rn 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.",

keywords = "Bayesian quadrature, Gaussian process regression, Mat{\'e}rn covariance, Scale mixture representation, State space approximation",

author = "Filip Tronarp and Toni Karvonen and Simo S{\"a}rkk{\"a}",

year = "2018",

month = oct,

day = "31",

doi = "10.1109/MLSP.2018.8516992",

language = "English",

volume = "2018-September",

series = "IEEE International Workshop on Machine Learning for Signal Processing",

publisher = "IEEE",

editor = "Nelly Pustelnik and Zheng-Hua Tan and Zhanyu Ma and Jan Larsen",

booktitle = "Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018",

address = "United States",

note = "IEEE International Workshop on Machine Learning for Signal Processing, MLSP ; Conference date: 17-09-2018 Through 20-09-2018",

}

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, IEEE, IEEE International Workshop on Machine Learning for Signal Processing, Aalborg, Denmark, 17/09/2018. https://doi.org/10.1109/MLSP.2018.8516992

Mixture representation of the matérn class with applications in state space approximations and Bayesian quadrature. / Tronarp, Filip; Karvonen, Toni; Särkkä, Simo.
Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018. ed. / Nelly Pustelnik; Zheng-Hua Tan; Zhanyu Ma; Jan Larsen. Vol. 2018-September IEEE, 2018. 8516992 (IEEE International Workshop on Machine Learning for Signal Processing).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Mixture representation of the matérn class with applications in state space approximations and Bayesian quadrature

AU - Tronarp, Filip

AU - Karvonen, Toni

AU - Särkkä, Simo

N1 - Conference code: 28

PY - 2018/10/31

Y1 - 2018/10/31

N2 - 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.

AB - 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.

KW - Bayesian quadrature

KW - Gaussian process regression

KW - Matérn covariance

KW - Scale mixture representation

KW - State space approximation

UR - http://www.scopus.com/inward/record.url?scp=85057002621&partnerID=8YFLogxK

U2 - 10.1109/MLSP.2018.8516992

DO - 10.1109/MLSP.2018.8516992

M3 - Conference contribution

AN - SCOPUS:85057002621

VL - 2018-September

T3 - IEEE International Workshop on Machine Learning for Signal Processing

BT - Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018

A2 - Pustelnik, Nelly

A2 - Tan, Zheng-Hua

A2 - Ma, Zhanyu

A2 - Larsen, Jan

PB - IEEE

T2 - IEEE International Workshop on Machine Learning for Signal Processing

Y2 - 17 September 2018 through 20 September 2018

ER -

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

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

Abstract

Publication series

Workshop

Keywords

Access to Document

OpenUrl availability

Other files and links

Fingerprint

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

Cite this

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

Abstract

Publication series

Workshop

Keywords

Access to Document

OpenUrl availability

Other files and links

Fingerprint

Projects

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

Cite this