Monitoring sparse and attributed networks with online Hurdle models

In this article we create a novel monitoring system to detect changes within a sequence of networks. Specifically, we consider sparse, weighted, directed, and attributed networks. Our approach uses the Hurdle model to capture sparsity and explain the weights of the edges as a function of the node and edge attributes. Here, the weight of an edge represents the number of interactions between two nodes. We then integrate the Hurdle model with a state-space model to capture temporal dynamics of the edge formation process. Estimation is performed using an extended Kalman Filter. Statistical process control charts are used to monitor the network sequence in real time in order to identify changes in connectivity patterns that are caused by regime shifts. We show that the proposed methodology outperforms alternative approaches on both synthetic and real data. We also perform a detailed case study on the 2007–2009 financial crisis. Demonstrating the promise of the proposed approach as an early warning system, we show that our method applied to financial interbank lending networks would have raised alarms to the public prior to key events and announcements by the European Central Bank.