This manuscript develops computationally efficient online learning for multivariate spatiotemporal models. The method relies on matrix-variate Gaussian distributions, dynamic linear models, and Bayesian predictive stacking to efficiently share information across temporal data shards. The model facilitates effective information propagation over time while seamlessly integrating spatial components within a dynamic framework, building a Markovian dependence structure between datasets at successive time instants. This structure supports flexible, high-dimensional modeling of complex dependence patterns, as commonly found in spatiotemporal phenomena, where computational challenges arise rapidly with increasing dimensions. The proposed approach further manages exact inference through predictive stacking, enhancing accuracy and interoperability. Combining sequential and parallel processing of temporal shards, each unit passes assimilated information forward, then back-smoothed to improve posterior estimates, incorporating all available information. This framework advances the scalability and adaptability of spatiotemporal modeling, making it suitable for dynamic, multivariate, and data-rich environments.

翻译：本文提出了一种计算高效的多元时空模型在线学习方法。该方法基于矩阵变量高斯分布、动态线性模型和贝叶斯预测堆叠，以在时间数据分片间高效共享信息。该模型在动态框架内无缝整合空间分量的同时，促进了信息随时间推移的有效传播，并在连续时间点的数据集之间建立了马尔可夫依赖结构。这种结构支持对复杂依赖模式（常见于时空现象中）进行灵活的高维建模，其中计算挑战随维数增加而迅速出现。所提出的方法通过预测堆叠进一步实现了精确推断，从而提高了准确性和互操作性。结合时间分片的顺序与并行处理，每个单元将同化信息前向传递，然后通过反向平滑以改进后验估计，并整合所有可用信息。该框架提升了时空建模的可扩展性与适应性，使其适用于动态、多元且数据丰富的环境。