Fast covariance-free spatiotemporal modeling via coarse-to-fine learning
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/).
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BibTeX
@misc{murakami2026fast,
title = {{Fast covariance-free spatiotemporal modeling via coarse-to-fine learning}},
author = {Daisuke Murakami},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.03449},
eprint = {2608.03449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03449},
}
RIS
TY - UNPB
TI - Fast covariance-free spatiotemporal modeling via coarse-to-fine learning
AU - Daisuke Murakami
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2608.03449
UR - https://arxiv.org/abs/2608.03449
AB - 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/).
ER -