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/).

翻译：本研究提出从粗到细的空间建模（CFSM）作为一种可扩展且与机器学习兼容的替代方案，以取代传统的空间过程模型。与传统的基于协方差的空间模型不同，CFSM使用局部模型的多尺度集合来表示空间过程。为确保模型训练的稳定性，首先对更易于学习的大尺度模式进行建模，随后再处理小尺度模式，一旦验证分数停止提升即终止训练。该基于保留验证的训练流程，可轻松与随机森林和神经网络等其他机器学习算法集成。CFSM训练在计算上具有高效性，因为它避免了显式矩阵求逆，而这正是传统空间高斯过程中的主要计算瓶颈。比较性蒙特卡洛实验表明，CFSM及其与随机森林的集成，相较于现有模型实现了更优的预测性能。最后，我们将所提方法应用于日本东京都市区住宅地价的分析中。CFSM已通过R包spCF实现（https://cran.r-project.org/web/packages/spCF/）。