  In this work, we are interested in structure learning for a set of spatially
distributed dynamical systems, where individual subsystems are coupled via
latent variables and observed through a filter. We represent this model as a
directed acyclic graph (DAG) that characterises the unidirectional coupling
between subsystems. Standard approaches to structure learning are not
applicable in this framework due to the hidden variables, however we can
exploit the properties of certain dynamical systems to formulate exact methods
based on state space reconstruction. We approach the problem by using
reconstruction theorems to analytically derive a tractable expression for the
KL-divergence of a candidate DAG from the observed dataset. We show this
measure can be decomposed as a function of two information-theoretic measures,
transfer entropy and stochastic interaction. We then present two mathematically
robust scoring functions based on transfer entropy and statistical independence
tests. These results support the previously held conjecture that transfer
entropy can be used to infer effective connectivity in complex networks.
