Directed Information Graphs: A generalization of Linear Dynamical Graphs

We study the relationship between Directed Information Graphs (DIG) and Linear Dynamical Graphs (LDG), both of which are graphical models where nodes represent scalar random processes. DIGs are based on directed information and represent the causal dynamics between processes in a stochastic system. LDGs capture causal dynamics but only in linear dynamical systems and there are Wiener filtering to do so in a subset of LDGs. This study shows that the DIGs are generalized version of the LDGs and any strictly causal LDGs can be reconstructed through learning the corresponding DIGs.