Monitoring network changes in social media

Econometricians are increasingly working with high-dimensional networks and their dynamics. Econometricians, however, are often confronted with unforeseen changes in network dynamics. In this article, we develop a method and the corresponding algorithm for monitoring changes in dynamic networks. We characterize two types of changes, edge-initiated and node-initiated, to feature the complexity of networks. The proposed approach accounts for three potential challenges in the analysis of networks. First, networks are high-dimensional objects causing the standard statistical tools to suffer from the curse of dimensionality. Second, any potential changes in social networks are likely driven by a few nodes or edges in the network. Third, in many dynamic network applications such as monitoring network connectedness or its centrality, it will be more practically applicable to detect the change in an online fashion than the offline version. The proposed detection method at each time point projects the entire network onto a low-dimensional vector by taking the sparsity into account, then sequentially detects the change by comparing consecutive estimates of the optimal projection direction. As long as the change is sizeable and persistent, the projected vectors will converge to the optimal one, leading to a jump in the sine angle distance between them. A change is therefore declared. Strong theoretical guarantees on both the false alarm rate and detection delays are derived in a sub-Gaussian setting, even under spatial and temporal dependence in the data stream. Numerical studies and an application to the social media messages network support the effectiveness of our method.