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.

翻译：我们提出了一种新颖且通用的方法，用于检测具有马尔可夫结构的动态网络中的多个变点，称为随机区间蒸馏（RID）。通过收集具有足够信号强度的随机区间，并将其重新组装成一系列信息丰富的短区间，结合稀疏通用奇异值阈值处理，我们的新方法能够在低秩网络中，无需任何关于最小间距的先验知识，在检测和定位边界方面达到与其独立对应方法近乎极小极大最优性，这与许多先前方法不同。特别地，受最近一个非渐近边界的启发，我们的方法利用邻接矩阵CUSUM的算子范数，并在无需先前方法所要求的样本分割的情况下实现了上述最优性。对于实际应用，我们引入了一种基于聚类和数据驱动的程序，利用RID与聚类之间的联系来确定信号强度的最优阈值。我们通过模拟和真实数据示例检验了我们方法的有效性和实用性。