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：生成式时序网络模型在分析复杂网络的依赖结构与演化模式中发挥着重要作用。由于真实网络数据的复杂性，通常难以假定其底层数据生成机制本身随时间保持不变。这一观察促使研究者关注演化网络分布结构中的变点或突变问题。本文提出一种基于似然的方法，用于检测无向仿射偏好依附网络中的变点，并建立了检测单个变点的假设检验框架，同时给出了变点的一致性估计量。该结果需要在存在长程依赖性的变点机制下，证明最大似然估计量的一致性与渐近正态性。通过滑动窗口方法和计算效率更高的得分统计量，本方法进一步扩展至多变点场景。我们通过仿真将所提方法与先前发展的非参数变点估计量进行比较，并将所发展的方法应用于模拟Twitter网络中话题流行度随时间演化的建模。