Fast covariance-free spatiotemporal modeling via coarse-to-fine learning

2026-08-04

AI Summary

This work addresses the limitations of traditional spatiotemporal modeling approaches, which rely on covariance structures that tightly couple spatial and temporal components, leading to high computational costs. The authors propose a coarse-to-fine spatiotemporal modeling framework (CF-STM) that, for the first time, decouples multiscale locally weighted spatial representations from local state-space temporal models, enabling efficient, covariance-free modeling. This decoupling allows flexible selection of temporal dynamics without altering the spatial structure, substantially enhancing model interpretability and computational efficiency. Empirical evaluations demonstrate that CF-STM achieves predictive accuracy comparable to existing scalable methods in Monte Carlo simulations while incurring lower computational overhead. Furthermore, when applied to Tokyo residential land price data, the framework effectively captures complex spatiotemporal evolution patterns.

Abstract

Scalable spatiotemporal modeling remains challenging because conventional methods rely on covariance models that tightly couple spatial representation and temporal inference, often leading to high computational costs. To address this difficulty, we developed coarse-to-fine spatiotemporal modeling (CF-STM), a framework that extends coarse-to-fine spatial modeling (CF-SM) to spatiotemporal settings. CF-STM represents latent spatial processes through multiscale locally weighted models, with temporal dependence modeled separately through state-space models defined at local centers. This covariance-free formulation achieves scalable computation while allowing temporal models to be flexibly specified without altering the spatial representation. Monte Carlo experiments demonstrate predictive performance comparable to that of alternative scalable space-time models at a substantially lower computational cost. An application to long-term residential land price data in the Tokyo metropolitan area shows that CF-STM flexibly captures complex spatiotemporal patterns while enabling interpretable inferences. CF-STM is implemented in an R package spCF (https://cran.r-project.org/web/packages/spCF/).

Problem

• spatiotemporal modeling
• scalability
• covariance models
• computational cost

Innovation

• covariance-free
• coarse-to-fine learning
• spatiotemporal modeling
• state-space models
• scalable computation