Adaptive Markovian Spatiotemporal Transfer Learning in Multivariate Bayesian Modeling

TL;DR

This paper introduces an efficient online Bayesian framework for multivariate spatiotemporal modeling that leverages Markovian dependence, matrix-variate Gaussian distributions, and predictive stacking to improve scalability and accuracy in high-dimensional dynamic data environments.

Contribution

It develops a novel adaptive Markovian transfer learning approach that integrates spatial and temporal information efficiently in multivariate Bayesian models.

Findings

Enhanced computational efficiency for high-dimensional spatiotemporal data

Improved accuracy through predictive stacking and smoothing techniques

Scalable framework suitable for dynamic, data-rich environments

Abstract

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.