In this paper we study online change point detection in dynamic networks with time heterogeneous missing pattern within networks and dependence across the time course. The missingness probabilities, the entrywise sparsity of networks, the rank of networks and the jump size in terms of the Frobenius norm, are all allowed to vary as functions of the pre-change sample size. On top of a thorough handling of all the model parameters, we notably allow the edges and missingness to be dependent. To the best of our knowledge, such general framework has not been rigorously nor systematically studied before in the literature. We propose a polynomial time change point detection algorithm, with a version of soft-impute algorithm (e.g. Mazumder et al., 2010; Klopp, 2015) as the imputation sub-routine. Piecing up these standard sub-routines algorithms, we are able to solve a brand new problem with sharp detection delay subject to an overall Type-I error control. Extensive numerical experiments are conducted demonstrating the outstanding performances of our proposed method in practice.

翻译：本文研究了在动态网络中，存在随时间变化的非均匀缺失模式以及跨时间依赖性的在线变化点检测问题。缺失概率、网络的逐元素稀疏性、网络的秩以及基于Frobenius范数的跳跃幅度，均被允许作为变化前样本大小的函数而变化。在对所有模型参数进行彻底处理的基础上，我们特别允许边和缺失性之间存在依赖性。据我们所知，文献中此前尚未对此类通用框架进行过严格且系统的研究。我们提出了一种多项式时间变化点检测算法，该算法采用soft-impute算法（例如Mazumder等人，2010；Klopp，2015）的变体作为插补子程序。通过整合这些标准子程序算法，我们能够在整体I型错误控制下，以敏锐的检测延迟解决一个全新的问题。大量数值实验表明，我们提出的方法在实践中具有卓越的性能。