Network structure identification from corrupt data streams

Complex networked systems can be modeled as graphs with nodes representing the agents and links describing the dynamic coupling between them. Previous work on network identification has shown that the network structure of linear time-invariant (LTI) systems can be reconstructed from the joint power spectrum of the data streams. These results assumed that data are perfectly measured. However, real-world data are subject to many corruptions, such as inaccurate time-stamps, noise, and data loss. We show that identifying the structure of linear time-invariant (LTI) systems using corrupt measurements results in the inference of erroneous links. We provide an exact characterization and prove that such erroneous links are restricted to the neighborhood of the perturbed node. We extend the analysis of LTI systems to the case of Markov random fields with corrupt measurements. We show that data corruption in Markov random fields results in spurious probabilistic relationships in precisely the locations, where spurious links arise in LTI systems.