Connecting graphical notions of separation and statistical notions of independence for topology reconstruction

Over the last decade, there has been a significant increase in interest for techniques that can infer the connectivity structure of a network of dynamic systems. This article examines a flexible class of network systems and reviews various methods for reconstructing their underlying graph. However, these techniques typically only guarantee consistent reconstruction if additional assumptions on the model are made, such as the network topology being a tree, the dynamics being strictly causal, or the absence of directed loops in the network. The central theme of the article is to reinterpret these methodologies under a unified framework where a graphical notion of separation between nodes of the underlying graph corresponds to a probabilistic notion of separation among associated stochastic processes.