Interpretable, predictive spatio-temporal models using supervised dimension reduction

Abstract

Spatio-temporal phenomena are often complicated, but kriging methods are widely used in modeling such data, where only a very simple mean structure is assumed. The key to the success of kriging methods is leaving all important process description to covariance functions. We can decompose its covariance function to have more understanding about the main temporal patterns shared by most locations or spatial structures repeated happen over time points. Although such factorization is simple, it is still not easy to imagine the functional forms. We instead develop a novel approach based on supervised dimension reduction for spatio-temporal data to capture nonlinear mean structures without requiring a pre-specified parametric model. In addition to prediction as a common interest, our approach focuses more on the exploration of geometric information in the data. The dimension reduction method of Pairwise Directions Estimation (PDE) is incorporated in our approach to implement the data-driven function searching of spatial structures and temporal patterns. The random effects not explained in the mean structures are still characterized by a standard kriging model. In many practical situations, our proposal can produce not only more explainable model formulation but also more accurate prediction. Illustrative applications to two real datasets are also presented. The results demonstrate that the proposed method is useful for exploring and interpreting the prominent trend for spatio-temporal data.?