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.
This paper proposes a model of spatio-temporal dynamics that modelsa global latent process that governs the interactions betweenhigh level clusters of points together with a local observed processin which interactions are decoupled from points outside of one's cluster.Both levels can be thought of as vector autoregressive models.The authors apply their method to modeling data from a numericalsimulation of a geologic model of fluid flow under the earth's subsurface.In general, this was a technically strong paper and shows off some state of the artoptimization techniques.  On the other hand it was also a difficult paper to get through asit was notation heavy and quite dense.  In particular, there are topicsthat are not typically ``NIPS'' topics, for which I think the authors should spendmore time providing intuition for.As an example, I do not have a good graspwhat it means to approximate the latentprocess with a 1-dimensional convection diffusion system --- the authors talk aboutthe computational benefits --- but what kind of behavior can we not capturewhen we make this approximation?The experimental setting seemed interesting but I would have liked to see some morediscussion about the task --- how was the training/test split performed inthis setting?  And how are errors measured? (The authors report errors in percentage,but it is unclear what the denominator here is).I would have also like to see more extensive experiments, particularly with more than one dataset,as it is difficult to understand if the proposed model is generally applicable or if itis specifically good for this fluid-flow setting.  Though spatio-temporal processesthat have interesting things happening at multiple scales are ubiquitous, the paperdoes make assumptions (such as the 1-dimensional convection-diffusion assumption again)that make the specific optimization approach tractable --- but the authors do notdiscuss other settings in which these assumptions might also apply.typos:Next in Section 3, relaxations to simply the problem along with with efficient algorithmfor parameter estimation are developed.unbalanced bracket on line 184page 5 second to last line (268) --- parentheses at wrong level for alpha^{(n)}grep for nonhierarchal and hierarchal -> nonhierarchical, hierarchical