An efficient implementation for spatial–temporal Gaussian process regression and its applications

Spatial–temporal Gaussian process regression is a popular method for spatial–temporal data modeling. Its state-of-art implementation based on the state-space model realization of and its corresponding Kalman filter smoother, has computational complexity O ( N M 3 ) , where are number time instants spatial input locations, respectively, thus can only be applied to with large but relatively small . In this paper, our primary goal show that by exploring Kronecker structure process, it possible further reduce + 2 proposed moderately The illustrated over applications in weather prediction spatially-distributed system identification. Our secondary design kernel both Colorado precipitation GHCN temperature data, such while having more efficient implementation, better performance also achieved than result.