Online network change point detection with missing values

In this paper we study online change point detection in dynamic networks with heterogeneous missing pattern across the networks and the time course. The missingness probabilities, the networks' entrywise sparsity, the rank of the networks and the jump size in terms of the Frobenius norm, are all allowed to vary as functions of the pre-change sample size. To the best of our knowledge, such general framework has not been rigorously studied before in the literature. We propose a polynomial-time change point detection algorithm, with a version of soft-impute algorithm (Mazumder et al., 2010; Klopp, 2015) as the imputation sub-routine. We investigate the fundamental limits of this problem and show that the detection delay of our algorithm is nearly optimal, saving for logarithmic factors, in some low-rank regimes, with a pre-specified tolerance on the probability of false alarms. Extensive numerical experiments are conducted demonstrating the outstanding performances of our proposed method in practice.