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 patterns within networks and dependence across both nodes and time. 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 temporally dependent. To the best of our knowledge, such a general framework has not been rigorously or systematically studied before in the literature. We propose a polynomial‐time change point detection algorithm, with a version of the soft‐impute algorithm as the imputation sub‐routine. By piecing up these established sub‐routines, our proposed algorithm achieves sharp detection delay while controlling the overall Type‐I error. Extensive numerical experiments support our theoretical findings and demonstrate the effectiveness of our proposed method in practice.