Inference in time series of graphs using locality statistics

We formulate change-point detection in a time series of graphs as a hypothesis testing problem in terms of Stochastic Block Model time series. We analyze two classes of scan statistics by deriving the limiting properties and power characteristics of the competing scan statistics. 1. Change-Point detection in Stochastic Block Model formulation Given a time series of graphs Gt = (V,Et), where the vertex set V = [n] = {1, · · · , n} is fixed throughout, an important inference task in time series analysis is to identify, from {Gt}, excessive communication activities in a subregion of a dynamic network. Statistically speaking, we want to test, for a given t ∈ N, the null hypothesis H0 that t is not a change-point against the alternative hypothesis HA that t is a change-point. We say that t ∗ is a change-point for {Gt} if there exists distinct choices of matrices P0, PA independent of t such that H0: Gt ∼ SBM(P0, {[ni]}) for all t, HA: Gt