This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to capture nonlinear mean structures without requiring a prespecified parametric model. In addition to prediction as a common interest, this approach emphasizes the exploration of geometric information from the data. The method of Pairwise Directions Estimation (PDE; Lue, 2019) is implemented in our approach as a data-driven function searching for spatial patterns and temporal trends. The benefit of using geometric information from the method of PDE is highlighted, which aids effectively in exploring data structures. We further enhance PDE, referring to it as PDE+, by incorporating kriging to estimate the random effects not explained in the mean functions. Our proposal can not only increase prediction accuracy, but also improve the interpretation for modeling. Two simulation examples are conducted and comparisons are made with four existing methods. The results demonstrate that the proposed PDE+ method is very useful for exploring and interpreting the patterns and trends for spatio-temporal data. Illustrative applications to two real datasets are also presented.
Harvard University, Institute for Quantitative Social Science（哈佛大学量化社会科学研究所）；Stockholm University Demography Unit（斯德哥尔摩大学人口学单位）；Malmö University, Department of Global Political Studies（马尔默大学全球政治研究系）；University of Catania, Department of Political and Social Sciences（卡塔尼亚大学政治与社会科学系）；University of Toronto, Graduate School of Public and International Affairs（多伦多大学公共与国际事务研究生院）
Clustering and Recognition of Spatiotemporal Features through Interpretable Embedding of Sequence to Sequence Recurrent Neural Networks
Department of Electrical & Computer Engineering（电气与计算机工程系）；Department of Applied Mathematics（应用数学系）；University of Washington（华盛顿大学）；Seattle, WA 98195（西雅图, WA 98195（注意：地址信息按要求不应提取，此处仅为示例说明））
Unifying Physics- and Data-Driven Modeling via Novel Causal Spatiotemporal Graph Neural Network for Interpretable Epidemic Forecasting
Frankfurt Institute for Advanced Studies（法兰克福高等研究院）；Goethe Universität Frankfurt（法兰克福大学）；Xidian-FIAS International Joint Research Center（西电-法兰克福高等研究院国际联合研究中心）；School of Science and Engineering, The Chinese University of Hong Kong（香港中文大学（深圳）理工学院）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）
Regression modelling of spatiotemporal extreme U.S. wildfires via partially-interpretable neural networks
School of Mathematics, University of Edinburgh（爱丁堡大学数学学院）；Statistics Program, Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学计算机、电气与数学科学与工程（CEMSE）分部统计项目）
Scalable Bayesian Spatiotemporal Tensor Modeling for Censored and Missing Areal Data
Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）；National Chung Hsing University（国立中兴大学）；China Medical University（中国医药大学）；University of Connecticut（康涅狄格大学）
