A0896
Title: Random interval distillation for detection of change-points in Markov chain Bernoulli networks
Authors: Xinyuan Fan - Tsinghua University (China) [presenting]
Weichi Wu - Tsinghua University (China)
Abstract: 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 universal singular value thresholding, the new approach can achieve a 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, the method utilizes the operator norm of CUSUMs of the adjacency matrices, achieving the aforementioned optimality without sample splitting as required by the previous method. For practical applications, a clustering-based and data-driven procedure is introduced to determine the optimal threshold for signal strength, utilizing the connection between RID and clustering. The effectiveness and usefulness of the methodology are examined via extensive simulation studies and a real data example.