Statistical Inference on Random Dot Product Graphs: a Survey
Statistical Inference on Random Dot Product Graphs: a Survey
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发表时间：
2017-09
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通讯作者：
A. Athreya;D. E. Fishkind;M. Tang;C. Priebe;Youngser Park;J. Vogelstein;Keith D. Levin;V. Lyzinski;Yichen Qin;D. Sussman
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作者：
A. Athreya;D. E. Fishkind;M. Tang;C. Priebe;Youngser Park;J. Vogelstein;Keith D. Levin;V. Lyzinski;Yichen Qin;D. Sussman
随机点积图（RDPG）是一种独立边随机图，它在分析上易于处理，同时包含或可以成功近似各种随机图，从相对简单的随机块模型到复杂的潜在位置图。在这篇调查论文中，我们描述了随机点积图统计推断的综合范式，该范式以邻接和拉普拉斯矩阵的谱嵌入为中心。我们研究了图推理中经典欧几里得推理的几个规范原则的类似物：特别是，我们总结了关于邻接和拉普拉斯谱嵌入的一致性和渐近正态性的现有结果，以及这些谱嵌入在构建图数据的单样本和多样本假设检验中可以发挥的作用。我们研究了一些现实世界的应用，包括大型社交网络中的社区检测和分类，以及通过果蝇连接组的探索性数据分析确定功能和生物学相关的网络属性。我们概述了谱图推理中必要的背景和当前未解决的问题。
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describe a comprehensive paradigm for statistical inference on random dot product graphs, a paradigm centered on spectral embeddings of adjacency and Laplacian matrices. We examine the analogues, in graph inference, of several canonical tenets of classical Euclidean inference: in particular, we summarize a body of existing results on the consistency and asymptotic normality of the adjacency and Laplacian spectral embeddings, and the role these spectral embeddings can play in the construction of single- and multi-sample hypothesis tests for graph data. We investigate several real-world applications, including community detection and classification in large social networks and the determination of functional and biologically relevant network properties from an exploratory data analysis of the Drosophila connectome. We outline requisite background and current open problems in spectral graph inference.