Private Online Community Detection for Censored Block Models

We study the private online change detection problem for dynamic communities, using a censored block model (CBM). Focusing on the notion of edge differential privacy (DP), we seek to understand the fundamental tradeoffs between the privacy budget, detection delay, and exact community recovery of community labels. We establish the theoretical lower bound on the delay in detecting changes privately and propose an algorithm capable of identifying changes in the community structure, while maintaining user privacy. Further, we provide theoretical guarantees for the effectiveness of our proposed method by showing necessary and sufficient conditions on change detection and exact recovery under edge DP. Simulation and real data examples are provided to validate the proposed method.