An Information Criterion for Inferring Coupling in Distributed Dynamical Systems
This work addresses the problem of inferring coupling in distributed dynamical systems for researchers in fields like physics or biology, but it appears incremental as it builds on existing structure learning procedures by focusing on global optimization.
The paper tackles the structure learning problem for spatially distributed dynamical systems coupled via a directed acyclic graph by exploiting dynamical system properties to compute globally optimal approximations of network structures, showing that the log-likelihood has an intuitive interpretation in terms of information transfer.
The behaviour of many real-world phenomena can be modelled by nonlinear 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 systems. 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.