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

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**Mixture representation of the matérn class with applications in state space approximations and Bayesian quadrature.** / Tronarp, Filip; Karvonen, Toni; Särkkä, Simo.

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

### Harvard

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

### APA

*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

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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

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

ER -

ID: 30375803