An efficient network reconstruction method and applications

Identifying the interconnections among modules in a dynamic network from observed data poses a significant challenge in many scientific disciplines. Many methods for network reconstruction from observational data significantly limit the type of systems they are considering. For example, Granger causality considers only networks with strictly causal dynamics, and methods from the graphical models literature are focused on reconstructing networks with static relationships. In this article, we focus on a novel network reconstruction method, called Mixed-Delay (MD) that can consistently reconstruct a wide class of linear dynamic networks that do not contain any algebraic loops. However, the steps in the MD algorithm are of combinatorial complexity. In this article, we propose an optimization to the MD method that yields the method more informative and polynomial for sparse networks, while preserving the theoretical guarantees of the method. We demonstrate the optimized MD method on simulated and real data. The first real-data application aims to reconstruct networks that show the spread of COVID-19 in the US. Then we apply the method on monthly average temperature data and reconstruct temperature relationships among states in the US, as well as European and South-East Asian countries.