基于由粗到细学习的快速无协方差时空建模
Fast covariance-free spatiotemporal modeling via coarse-to-fine learning
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中文总结 AI 辅助
针对传统时空建模计算成本高的问题，提出将CF-SM扩展至时空场景的CF-STM框架，通过多尺度局部加权模型与局部中心状态空间模型分离建模时空，在保持预测性能的同时降低计算成本，且已实现为R包spCF。
中文摘要 AI 辅助
可扩展时空建模仍具挑战性，因为传统方法依赖协方差模型，该模型紧密耦合空间表示与时间推理，常导致高计算成本。为解决此难题，我们开发了由粗到细时空建模（CF-STM），这是一个将由粗到细空间建模（CF-SM）扩展至时空场景的框架。CF-STM通过多尺度局部加权模型表示潜在空间过程，在局部中心定义的状态空间模型单独建模时间依赖。这种无协方差公式实现了可扩展计算，同时允许灵活指定时间模型而不改变空间表示。蒙特卡洛实验表明，其预测性能与其他可扩展时空模型相当，但计算成本显著更低。将其应用于东京都市圈长期住宅地价数据，显示CF-STM可灵活捕捉复杂时空模式，同时支持可解释推理。CF-STM已在R包spCF中实现。
英文摘要
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/).
发表机构
- Institute of Statistical Mathematics, Japan（日本统计数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
