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Nonstationary nonseparable random fields

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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:
DateEvent
2020Available
1 June 2020Accepted
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 IDRIOXX Funder NameFunder ID
UNSPECIFIEDLloyd’s Register Foundation https://www.lr.org/en-gb/
PhD fellowshipAlan Turing Institutehttp://dx.doi.org/10.13039/100012338
EP/N510129/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIEDMicrosofthttp://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
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