Effects of Data Corruption on Network Identification Using Directed Information

Complex networked systems can be modeled and represented as graphs, with nodes representing the agents and the links describing the dynamic coupling between them. The fundamental objective of network identification for dynamic systems is to identify causal influence pathways. However, dynamically related data streams that originate from different sources are prone to corruption caused by asynchronous time-stamps, packet drops, and noise. In this article, we show that identifying causal structure using corrupt measurements results in the inference of spurious links. A necessary and sufficient condition that delineates the effects of corruption on a set of nodes is obtained. Our theory applies to nonlinear systems, and systems with feedback loops. Our results are obtained by the analysis of conditional directed information (DI) in dynamic Bayesian networks. We provide consistency results for the conditional DI estimator that we use by showing almost-sure convergence.