Exponential-Family Models of Random Graphs: Inference in Finite, Super and Infinite Population Scenarios
Exponential-Family Models of Random Graphs: Inference in Finite, Super and Infinite Population Scenarios
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DOI：
10.1214/19-sts743
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发表时间：
2020-11-01
影响因子：
5.7
通讯作者：
Stewart, Jonathan R.
中科院分区：
文献类型：
--
作者：
Schweinberger, Michael;Krivitsky, Pavel N.;Stewart, Jonathan R.
指数族随机图模型（ERGM）构成了一个大型的统计框架，用于建模具有短尾或长尾度分布、协变量效应和广泛复杂依赖关系的密集和稀疏随机图。ERGM的特殊情况包括广义线性模型（GLM）、伯努利随机图、β模型、p（1）模型以及与空间统计和图像处理中的马尔可夫随机场相关的模型的网络等价物。虽然ERGMs在实践中被广泛使用，但人们对其理论特性提出了质疑。这些问题包括一些ERGM是近简并的，许多ERGM是非投射的。为了解决这些问题，必须仔细注意模型的规格和它们的基本假设，并在模型中使用的推理设置。正如我们所讨论的，近简并可以影响缺乏结构的简单ERGM，但具有额外结构的适定性ERGM可以表现良好。同样，缺乏投射性会影响非似然推理，但基于似然的推理不需要投射性。在这里，我们审查适定性ERGM沿着与基于似然性的推理。我们首先澄清了ERGM框架中的“样本”和“人口”的核心统计概念，将生成人口图的过程与观察过程分开。然后，我们回顾了有限，超级和无限人口的情况下，基于似然推理。我们得出一致性结果，并应用于人脑网络。
Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling dense and sparse random graphs with short- or long-tailed degree distributions, covariate effects and a wide range of complex dependencies. Special cases of ERGMs include network equivalents of generalized linear models (GLMs), Bernoulli random graphs, beta-models, p(1)-models and models related to Markov random fields in spatial statistics and image processing. While ERGMs are widely used in practice, questions have been raised about their theoretical properties. These include concerns that some ERGMs are near-degenerate and that many ERGMs are non-projective. To address such questions, careful attention must be paid to model specifications and their underlying assumptions, and to the inferential settings in which models are employed. As we discuss, near-degeneracy can affect simplistic ERGMs lacking structure, but well-posed ERGMs with additional structure can be well-behaved. Likewise, lack of projectivity can affect non-likelihood-based inference, but likelihood-based inference does not require projectivity. Here, we review well-posed ERGMs along with likelihood-based inference. We first clarify the core statistical notions of "sample" and "population" in the ERGM framework, separating the process that generates the population graph from the observation process. We then review likelihood-based inference in finite, super and infinite population scenarios. We conclude with consistency results, and an application to human brain networks.