Online network change point detection with missing values and temporal dependence

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.