Random Interval Distillation for Detection of Change-Points in Markov Chain Bernoulli Networks

Abstract

We propose a new and generic approach for detecting multiple change-points in dynamic networks with Markov formation, termed random interval distillation (RID). By collecting random intervals with sufficient strength of signals and reassembling them into a sequence of informative short intervals, together with sparse universal singular value thresholding, our new approach can achieve nearly minimax optimality as their independent counterparts for both detection and localization bounds in low-rank networks without any prior knowledge about minimal spacing, which is unlike many previous methods. In particular, motivated by a recent nonasymptotic bound, our method uses the operator norm of CUSUMs of the adjacency matrices, and achieves the aforementioned optimality without sample splitting as required by the previous method. For practical applications, we introduce a clustering-based and data-driven procedure to determine the optimal threshold for signal strength, utilizing the connection between RID and clustering. We examine the effectiveness and usefulness of our methodology via simulations and a real data example.