Deep Spatially Varying Coefficient Model for Interpolation of Non‐Stationary Meteorological Data

Abstract

In spatial statistics, the spatially varying coefficient model (SVCM) is widely applied in the analysis and interpolation of non‐stationary spatial data. By incorporating spatially varying coefficients, the model can capture spatial heterogeneity and provide an attractive interpretation of response‐covariate associations. However, intensive matrix operations are inevitable in the inference of SVCM, which limits its scalability to massive spatial datasets. In contrast, deep learning has demonstrated considerable potential in various regression and classification tasks with large‐scale data in terms of accuracy and computational efficiency. Nevertheless, many deep learning models fail to capture the spatial variability when directly applied to non‐stationary spatial data and often lack interpretability. To address these challenges, we propose a deep spatially varying coefficient model (DSVCM) that combines the strengths of SVCM and deep learning. The proposed model aims to provide a computationally efficient interpolation method for non‐stationary spatial data, while also facilitating the interpretation of the effects of input covariates. In the proposed model, a deep neural network (DNN) is utilized to estimate spatially varying coefficients and responses, where spatial basis functions are served as input to capture spatial variability. By leveraging spatial basis functions, we establish the connection between DSVCM and SVCM, and theoretically prove the superiority of DSVCM in prediction accuracy. The effectiveness of the model is further demonstrated through extensive simulation studies and experiments on Singapore air temperature data. The results show that the proposed DSVCM outperforms several baseline models for spatial interpolation in both prediction accuracy and computational efficiency.