Abstract

Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) enhance their effectiveness by integrating both spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional challenges, such as dynamic spatial dimensions and partial observations, commonly encountered in scenarios like disease spread analysis and environmental monitoring. Furthermore, tracking high-dimensional targets with complex spatiotemporal interactions over extended periods is particularly challenging in terms of accuracy, efficiency, and computational feasibility. Given these challenges, a scalable online learning algorithm that is generically applicable to hidden STMRF (HSTMRF) models, with or without time-varying dimensions, remains an open problem. To address this gap, we introduce the Variable Target MRF Scalable Particle Filter (VT-MRF-SPF), a fully online learning algorithm designed for high-dimensional target tracking over HSTMRFs with time-varying dimensions. We rigorously guarantee the algorithmic performance, explicitly demonstrating its capability to overcome the curse of dimensionality. Additionally, we provide practical guidelines for tuning graphical parameters, leading to superior performance as evidenced by extensive examinations.