Structure recovery and trend estimation for dynamic network analysis

Low-dimensional parametric models for network dynamics have been successful as inferentially efficient and interpretable tools for modelling network evolution but have difficulty in settings with strong time inhomogeneity (particularly when sharp variation in parameters is possible and covariates are limited). Here, we propose to address this problem via a novel family of block-structured dynamic exponential-family random graph models (ERGMs), where the time domain is divided into consecutive blocks and the network parameters are assumed to evolve smoothly within each block. In particular, we let the latent ERGM parameters follow a piecewise polynomial model with an unknown block structure (e.g., change points). We propose an iterative estimation procedure that involves estimating the block structure using trend filtering and fitting ERGMs for networks belonging to the same time block. We demonstrate the utility of the proposed approach using simulation studies and applications to interbank transaction networks and citations among political blogs over the course of an electoral cycle.