Optimal change point detection and localization in sparse dynamic networks

We study the problem of change point localization in dynamic networks models. assume that we observe a sequence independent adjacency matrices same size, each corresponding to realization an unknown inhomogeneous Bernoulli model. The underlying distribution are piecewise constant, and may over subset time points, called points. concerned with recovering number positions In our model setting, allow for all parameters total including network minimal spacing between consecutive magnitude smallest degree sparsity networks. first identify region impossibility space such no estimator is provably consistent if data generated according falling region. propose computationally-simple algorithm localization, binary segmentation, relies on weighted averages matrices. show segmentation range nearly cover complement region, thus demonstrating existence phase transition at hand. Next, devise more sophisticated based singular value thresholding, local refinement, delivers accurate estimates locations. Under appropriate conditions, refinement guarantees minimax optimal rate while remaining computationally feasible.