Variational Propagation for Exact Spatiotemporal Dynamic Modeling

We introduce a novel approach for online learning in spatiotemporal models, leveraging variational propagation for exact inference. We integrate dynamic linear models with Bayesian predictive stacking to model spatiotemporal dependencies while maintaining scalability. The matrix-variate Gaussian distribution formulation enables efficient representation of spatial dependencies, while Bayesian predictive stacking addresses challenges associated with weakly identifiable parameters, improving both estimation and predictive accuracy by assimilating multiple models. Our methodology ensures posterior-to-prior updates by utilizing matrix-normal inverse-Wishart conjugacy and variational approximations. Through simulations, we demonstrate the efficacy and adaptability of our approach. Our findings highlight the potential of variational propagation in achieving exact, scalable inference for complex, data-rich environments. This work advances online learning in spatiotemporal modeling, offering a rapid framework for dynamic data analysis.