Statistical Consistency for Change Point Detection and Community Estimation in Time-Evolving Dynamic Networks

Suppose a time sequence of networks is observed. It is known that the probabilistic behaviors of the networks do not change over time, except at a few time points. These time points are usually called change points, whose number and locations are unknown. This paper proposes a method for automatically estimating such change points and the community structures of the networks. The proposed method invokes the minimum description length principle to derive a model selection criterion, where the best estimates are defined as its minimizer. It is shown that this selection criterion yields consistent estimates for the change points as well as the community structures. For practical minimization of the selection criterion, a bottom-up search algorithm that combines the EM-algorithm with variational approximation is developed. The promising empirical properties of the proposed method are illustrated via a sequence of numerical experiments and applications to some real datasets. To the best of the authors' knowledge, this method is one of the earliest that provides consistent estimates in the context of change point detection for time-evolving networks.