Efficient Recursive Implementation of Spatial-Temporal Gaussian Process Regression
作者单位：School of Science and Engineering and Shenzhen Research Institute of Big Data The Chinese University of Hong Kong The Experimental School of Shen Zhen Institute of Advanced Technology
会议名称：《第三十九届中国控制会议》
会议日期：2020年
学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学]
关 键 词：System identification Spatial-temporal data Big data Gaussian process regression kernel methods Kalman filter and smoother
摘 要：The current implementation of the spatial-temporal Gaussian process regression has computational complexity O(NM),where N and M are the number of temporal and spatial data,respectively,and thus can only be applied to data with large N but relatively small *** this work,we show that by exploring the Kronecker structure in the state-space model realization of the spatial-temporal Gaussian process,we can extend the current implementation with a coordinate transformation and an output transformation(corresponding to data preprocessing),such that the computational complexity is reduced to O(M+NM+NM) and therefore the proposed implementation can be applied to data with large N and moderately large ***,the proposed implementation can be parallelized and the computational complexity can be further lowered if parallel computing is adopted.