Wang, Kangrui, Hamelijnck, Oliver, Damoulas, Theodoros and Steel, Mark F. J. (2020) Nonstationary nonseparable random fields. In: 37th International Conference on Machine Learning, Remote, 12-18 Jul 2020. Published in: Proceedings of the 37 th International Conference on Machine Learning, 119 (In Press)

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Abstract

We describe a framework for constructing nonsta- tionary nonseparable random fields that are based on an infinite mixture of convolved stochastic processes. When the mixing process is station- ary but the convolution function is nonstationary we arrive at nonseparable kernels with constant non-separability that are available in closed form. When the mixing is nonstationary and the convolu- tion function is stationary we arrive at nonsepara- ble random fields that have varying nonseparabil- ity and better preserve local structure. These fields have natural interpretations through the spectral representation of stochastic differential equations (SDEs) and are demonstrated on a range of syn- thetic benchmarks and spatio-temporal applica- tions in geostatistics and machine learning. We show how a single Gaussian process (GP) with these random fields can computationally and sta- tistically outperform both separable and existing nonstationary nonseparable approaches such as treed GPs and deep GP constructions.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Random fields, Machine learning, Spatial analysis (Statistics), Stochastic processes
Journal or Publication Title:	Proceedings of the 37 th International Conference on Machine Learning
Official Date:	2020
Dates:	Date Event 2020 Available 1 June 2020 Accepted
Date of first compliant deposit:	9 June 2020
Volume:	119
Status:	Peer Reviewed
Publication Status:	In Press
Access rights to Published version:	Open Access
Copyright Holders:	Copyright 2020 by the author(s)
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID UNSPECIFIED Lloyd’s Register Foundation https://www.lr.org/en-gb/ PhD fellowship Alan Turing Institute http://dx.doi.org/10.13039/100012338 EP/N510129/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266 UNSPECIFIED Microsoft http://dx.doi.org/10.13039/100004318
Conference Paper Type:	Paper
Title of Event:	37th International Conference on Machine Learning
Type of Event:	Conference
Location of Event:	Remote
Date(s) of Event:	12-18 Jul 2020
Related URLs:	Organisation

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