复杂脑网络的指数随机图建模
Exponential Random Graph Modeling for Complex Brain Networks
摘要：
指数随机图模型（Exponential random graph models，ERGM），也被称为p* 模型，在社会科学文献中被广泛用于研究复杂网络及其全局结构如何依赖于底层结构组件。然而，关于它们在生物网络（特别是大脑网络）中的应用的文献仍然很少。基于图的特定特征（聚类系数、度分布等）的描述性模型已经主导了神经科学中的连通性研究。相应的生成模型已被开发，以重现这些功能之一。然而，全脑网络数据固有的复杂性需要开发和使用工具，以便同时系统地探索几个功能以及它们如何相互作用以形成全球网络架构。ERGM提供了一种统计原则方法来评估一组相互作用的局部大脑网络特征如何产生全局结构。我们说明了实用的ERGMs的建模，分析和模拟复杂的全脑网络与网络数据正常受试者。我们还提供了一个基础，通过实施和评估三种选择方法：传统的基于p值的向后选择方法，信息准则方法（AIC），和图形拟合优度（GOF）的方法选择重要的本地功能。图形GOF方法是最好的方法，因为科学家们对能够捕获和再现拟合的大脑网络的结构感兴趣。
英文摘要：
Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks.
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