The behavior of many real-world phenomena can be modeled by non-linear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical system. Specifically, we study the structure learning problem for spatially distributed dynamical systems coupled via a directed acyclic graph. Unlike established structure learning procedures that find locally maximum posterior probabilities of a network structure containing latent variables, our work exploits the properties of dynamical systems to compute globally optimal approximations of these distributions. We arrive at this result by the use of time delay embedding theorems. Taking an information-theoretic perspective, we show that the log-likelihood has an intuitive interpretation in terms of information transfer.
An Information Criterion for Inferring Coupling of Distributed Dynamical Systems
Oliver M. Cliff, Mikhail Prokopenko and Robert Fitch
Front. Robot. AI, 28 November 2016 | http://dx.doi.org/10.3389/frobt.2016.00071