Inference for time series of networks often relies on accurate vertex correspondence between network realizations at different times. In practice, however, such vertex alignments can be misspecified or unknown. We study the impact of vertex alignment on changepoint localization for dynamic networks through two illustrative models, each with a similar changepoint, with the key distinction being whether changepoint information is contained in marginal or joint distributions of the time-varying latent positions. We compare localization techniques ranging from the simple network statistic of average degree to the modern procedure of Euclidean mirrors. In one model, vertex misalignment causes little error, and in the other, it impairs localization in ways that cannot be corrected through graph matching or optimal transport, which we show are closely related in this setting. Our results demonstrate that robust network inference necessitates reckoning with the subtle interplay of marginal and joint information in the observed network time series.

翻译：网络时间序列的推断通常依赖于不同时间网络实现之间准确的顶点对应关系。然而在实际应用中，这种顶点对齐可能存在误配或未知的情况。我们通过两个说明性模型研究顶点对齐对动态网络变点定位的影响，这两个模型具有相似的变点，其关键区别在于变点信息是包含在时变潜在位置的边际分布还是联合分布中。我们比较了从简单的网络统计量（如平均度）到现代方法（如欧几里得镜像）的定位技术。在一个模型中，顶点错位几乎不引起误差；而在另一个模型中，这种错位会损害定位能力，且无法通过图匹配或最优传输（我们证明两者在此场景下密切相关）加以修正。我们的结果表明，要实现稳健的网络推断，必须考量观测网络时间序列中边际信息与联合信息之间微妙的相互作用。