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

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openAccess
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Conference article in proceedings
Date
2018-10-31
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Language
en
Pages
6
Series
Proceedings of the 2018 IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2018, Volume 2018-September, IEEE International Workshop on Machine Learning for Signal Processing
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.
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Keywords
Bayesian quadrature, Gaussian process regression, Matérn covariance, Scale mixture representation, State space approximation
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Citation
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