Coarse-to-Fine Spatial Modeling: A Scalable, Machine-Learning-Compatible Framework

Abstract

This study proposes coarse-to-fine spatial modeling (CFSM) as a scalable and machine learning-compatible alternative to conventional spatial process models. Unlike conventional covariance-based spatial models, CFSM represents spatial processes using a multiscale ensemble of local models. To ensure stable model training, larger-scale patterns that are easier to learn are modeled first, followed by smaller-scale patterns, with training terminated once the validation score stops improving. The training procedure, which is based on holdout validation, can be easily integrated with other machine learning algorithms, including random forests and neural networks. CFSM training is computationally efficient because it avoids explicit matrix inversion, which is a major computational bottleneck in conventional spatial Gaussian processes. Comparative Monte Carlo experiments demonstrated that the CFSM, as well as its integration with random forests, achieved superior predictive performance compared to existing models. Finally, we applied the proposed methods to an analysis of residential land prices in the Tokyo metropolitan area, Japan. The CFSM is implemented in an R package spCF ( https://cran.r-project.org/web/packages/spCF/).