  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.
