Projects per year

### 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 |
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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 |

Number of pages | 6 |

Volume | 2018-September |

ISBN (Electronic) | 9781538654774 |

DOIs | |

Publication status | Published - 31 Oct 2018 |

MoE publication type | A4 Article in a conference publication |

Event | IEEE International Workshop on Machine Learning for Signal Processing - Aalborg, Denmark Duration: 17 Sep 2018 → 20 Sep 2018 Conference number: 28 |

### Publication series

Name | IEEE International Workshop on Machine Learning for Signal Processing |
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Publisher | IEEE |

ISSN (Print) | 2161-0363 |

ISSN (Electronic) | 2161-0371 |

### Workshop

Workshop | IEEE International Workshop on Machine Learning for Signal Processing |
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Abbreviated title | MLSP |

Country | Denmark |

City | Aalborg |

Period | 17/09/2018 → 20/09/2018 |

### Keywords

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

## Projects

- 1 Finished

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

01/06/2015 → 31/08/2018

Project: Academy of Finland: Other research funding

## Cite this

*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