Reconstruction of Dynamic Networks with Cycles Using Partial Ancestral Graphs and Properties of Wiener Filters

Identifying the network structure of complex systems from observational data is of prime interest in many fields of science. In this article, we explore the problem of reconstruction of linear dynamic networks that contain cycles. Using partial ancestral graph (PAG) and skeleton/topology of the underlying generative structure we show that true orientation of edges in a network with cycles can be inferred correctly. Many ancestry and descendant relationships between the measured quantities in networked systems can be identified using PAG, whereas the skeleton of a network entail the connectivity among the quantities without specific directionality of the influence. However, together a PAG and skeleton can entail true edge directions in a generative structure. An algorithm to identify structures with cycles is developed using PAG and properties of Wiener filters. Simulation results are presented to show the efficacy of the algorithm.