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 naive 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. Such results require establishing consistency and asymptotic normality of the MLE under the changepoint regime, which suffers from long range dependence. 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.

翻译：生成式时变网络模型在分析复杂网络的依赖结构和演化模式中发挥着重要作用。由于真实网络数据的复杂性，通常不宜假定底层数据生成机制随时间保持不变。这一观察引发了对演化网络分布结构突变点或突变现象的研究。本文提出一种基于似然的方法来检测无向仿射偏好附着网络中的变点，并建立用于检测单一变点的假设检验框架，同时给出变点的一致估计量。这些结果需要建立在变点机制下极大似然估计的一致性和渐近正态性——该机制存在长程依赖性。随后通过滑动窗口方法和计算效率更高的得分统计量将该方法推广至多变点场景。本文还将所提方法与先前发展的非参数变点估计量进行模拟比较，并将所开发的方法应用于Twitter网络中主题流行度随时间演化的建模。