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An efficient implementation for spatial-temporal Gaussian process regression and its applications
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DOI：10.1016/j.automatica.2022.110679.png)
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摘要
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Spatial-temporal Gaussian process regression is a popular method for spatial-temporal data modeling. Its state-of-art implementation is based on the state-space model realization of the spatial-temporal Gaussian process and its corresponding Kalman filter and smoother, and has computational complexity O(NM3), where N and M are the number of time instants and spatial input locations, respectively, and thus can only be applied to data with large N but relatively small M. In this paper, our primary goal is to show that by exploring the Kronecker structure of the state-space model realization of the spatial-temporal Gaussian process, it is possible to further reduce the computational complexity to O(M3 + NM2) and thus the proposed implementation can be applied to data with large N and moderately large M. The proposed implementation is illustrated over applications in weather data prediction and spatially-distributed system identification. Our secondary goal is to design a kernel for both the Colorado precipitation data and the GHCN temperature data, such that while having more efficient implementation, better prediction performance can also be achieved than the state-of-art result. (c) 2022 Elsevier Ltd. All rights reserved.
Keyword:
Large scale spatial-temporal data
Gaussian process regression
Kalman filter and smoother
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期刊
IF:
5.9
论文数:
1.2W
被引数:
5.2W
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