An Efficient Implementation for Spatial-Temporal Gaussian Process Regression and Its Applications

2022/09/26 by Zhang, Junpeng, Ju, Yue, Mu, Biqiang +2 · 3 citations
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2209.12565

Abstract

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.

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