Likelihood-based Changepoint Detection in Preferential Attachment Networks

Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often na\"ive to assume that the underlying data-generative mechanism itself is invariant with time. Such observation leads to the study of changepoints or sudden shifts in the distributional structure of the evolving network. In this paper, we propose a likelihood-based methodology to detect changepoints in undirected, affine preferential attachment networks, and establish a hypothesis testing framework to detect a single changepoint, together with a consistent estimator for the changepoint. The methodology is then extended to the multiple changepoint setting via both a sliding window method and a more computationally efficient score statistic. We also compare the proposed methodology with previously developed non-parametric estimators of the changepoint via simulation, and the methods developed herein are applied to modeling the popularity of a topic in a Twitter network over time.