Network reconstruction from binary-state time series in presence of time delay and hidden nodes

摘要

Complex networks with binary-state dynamics represent many meaningful behaviors in a variety of contexts. Reconstruction of networked systems hosting delayed binary processes with hidden nodes becomes an outstanding challenge in this field. To address this issue, we extend the statistical inference method to complex networked systems with distinct binary-state dynamics in presence of time delay and missing data. By exploiting the expectation-maximization (EM) algorithm, we implement the statistical inference based approach to different (i.e., random, small world, and scale-free) networks hosting delayed-binary processes. Our framework is completely data driven, and does not require any a prior knowledge about the detailed dynamical process on the network; especially, our method can independently infer each physical connectivity and estimate the time delay solely from the data of a pair of nodes in this link. We provide a physical understanding of the underlying mechanism; and extensive numerical simulations validate the robustness, efficiency, and accuracy of our method.