Multi-scale Graphical Models for Spatio-Temporal Processes

Learning the dependency structure between spatially distributed observations of a spatio-temporal process is an important problem in many fields such as geology, geophysics, atmospheric sciences, oceanography, etc.. However, estimation of such systems is complicated by the fact that they exhibit dynamics at multiple scales of space and time arising due to a combination of diffusion and convection/advection [17]. As we show, time-series graphical models based on vector auto-regressive processes[18] are inefficient in capturing such multi-scale structure. In this paper, we present a hierarchical graphical model with physically derived priors that better represents the multi-scale character of these dynamical systems. We also propose algorithms to efficiently estimate the interaction structure from data. We demonstrate results on a general class of problems arising in exploration geophysics by discovering graphical structure that is physically meaningful and provide evidence of its advantages over alternative approaches.