通过子图采样进行模体估计：第四矩现象
Motif Estimation via Subgraph Sampling: The Fourth Moment Phenomenon
AI总结：
本文提出了一个在子图采样模型下对网络模体进行统计推断的框架，推导了Horvitz-Thompson估计量一致性与渐近正态性的充要条件，揭示了第四矩现象，并确定了多种图系综中的精确阈值。
摘要：
网络采样是理解大型复杂网络特征不可或缺的工具，因为在整个图上进行搜索在实践中是不可能的。在本文中，我们开发了一个用于统计推断的框架，用于在广泛使用的子图采样模型中对网络模体（如边、三角形和楔形）进行计数，其中每个顶点被独立采样，并观察到由采样顶点诱导的子图。我们推导了自然 Horvitz-Thompson (HT) 估计量的一致性和渐近正态性的充分必要条件，这可用于基于采样图构建置信区间和假设检验。特别地，我们证明了 HT 估计量的渐近正态性表现出有趣的第四矩现象，即只要 HT 估计量（经过适当的中心化和重缩放）的第四矩收敛到 3（标准正态分布的第四矩），它就依分布收敛到标准正态。作为推论，我们在各种自然图系综中推导了 HT 估计量一致性和渐近正态性的精确阈值，例如有界度的稀疏图、Erdos-Renyi 随机图、随机正则图和密集图子。
英文摘要：
Network sampling is an indispensable tool for understanding features of large complex networks where it is practically impossible to search over the entire graph. In this paper, we develop a framework for statistical inference for counting network motifs, such as edges, triangles, and wedges, in the widely used subgraph sampling model, where each vertex is sampled independently, and the subgraph induced by the sampled vertices is observed. We derive necessary and sufficient conditions for the consistency and the asymptotic normality of the natural Horvitz-Thompson (HT) estimator, which can be used for constructing confidence intervals and hypothesis testing for the motif counts based on the sampled graph. In particular, we show that the asymptotic normality of the HT estimator exhibits an interesting fourth-moment phenomenon, which asserts that the HT estimator (appropriately centered and rescaled) converges in distribution to the standard normal whenever its fourth-moment converges to 3 (the fourth-moment of the standard normal distribution). As a consequence, we derive the exact thresholds for consistency and asymptotic normality of the HT estimator in various natural graph ensembles, such as sparse graphs with bounded degree, Erdos-Renyi random graphs, random regular graphs, and dense graphons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
