An efficient implementation for spatial–temporal Gaussian process regression and its applications. (January 2023) - Zhang, Junpeng; Ju, Yue; Mu, Biqiang; Zhong, Renxin; Chen, Tianshi
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 ( N M 3 ), 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 ( M 3 + N M 2 ) 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.