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Wang, Kangrui, Hamelijnck, Oliver, Damoulas, Theodoros and Steel, Mark F. J. (2020) Non-separable non-stationary random fields. In: 37th International Conference on Machine Learning, ICML 2020, Remote, 13-18 Jul 2020. Published in: Proceedings of the 37th International Conference on Machine Learning, 119 pp. 9887-9897.
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Official URL: http://proceedings.mlr.press/v119/wang20g/wang20g....
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) | |||||||||||||||
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| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Statistics |
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| Library of Congress Subject Headings (LCSH): | Random fields, Machine learning, Spatial analysis (Statistics), Stochastic processes | |||||||||||||||
| Series Name: | Proceedings of Machine Learning Research | |||||||||||||||
| Journal or Publication Title: | Proceedings of the 37th International Conference on Machine Learning | |||||||||||||||
| Publisher: | PMLR | |||||||||||||||
| Official Date: | 2020 | |||||||||||||||
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| Volume: | 119 | |||||||||||||||
| Page Range: | pp. 9887-9897 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Access rights to Published version: | Open Access | |||||||||||||||
| Copyright Holders: | Copyright 2020 by the author(s) | |||||||||||||||
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| Conference Paper Type: | Paper | |||||||||||||||
| Title of Event: | 37th International Conference on Machine Learning, ICML 2020 | |||||||||||||||
| Type of Event: | Conference | |||||||||||||||
| Location of Event: | Remote | |||||||||||||||
| Date(s) of Event: | 13-18 Jul 2020 | |||||||||||||||
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