提出可比较参数化网络族的新度量方法，适用于动态社交网络与随机图模型。
Metrics for Parametric Families of Networks
- 基于变体最优传输构造参数化网络距离，统一多种已有度量
- 给出计算可行的下界，并与经典图统计量相关联
- 在随机图与度量空间中可一致逼近，适合建模演化数据
我们提出一个通用框架，用于分析参数化网络族的数据。基于最优传输的Gromov-Wasserstein变体，定义了一类参数化Gromov-Wasserstein距离，可用于比较时间演化度量空间（如群体运动）、随时间变化的加权社交网络及随机图模型。我们建立了这些距离的基本性质，证明其涵盖文献中若干现有度量，并推导出理论近似保证。特别地，我们设计了计算上可行的下界，并将其与随机图理论中常用的图统计量关联。此外，我们在随机图与随机度量空间设定下，证明了该距离可通过生成模型的样本估计实现一致逼近。最后，通过一系列数值实验展示了该框架的实际效用。
原文摘要 · Abstract (English)
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing such parametric data, including time-varying metric spaces induced by collective motion, temporally evolving weighted social networks, and random graph models. We establish foundational properties of these distances, showing that they subsume several existing metrics in the literature, and derive theoretical approximation guarantees. In particular, we develop computationally tractable lower bounds and relate them to graph statistics commonly used in random graph theory. Furthermore, we prove that our distances can be consistently approximated in random graph and random metric space settings via empirical estimates from generative models. Finally, we demonstrate the practical utility of our framework through a series of numerical experiments.
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