Modeling and Inference for Data with Network Dependency

在许多科学领域中，越来越多地遇到以网络为特征的复杂人际依赖数据。例如，在一些针对在校学生的调查研究中，除了在每个单元收集的传统变量（如吸毒、吸烟和心理健康状况）之外，还可能收集学生之间的友谊网络。感兴趣的反应，如药物使用，很可能通过友谊网络具有跨单位的依赖性。作为另一个例子，脑功能连接研究一直发现脑区域之间的功能联系，其中脑区域之间的依赖性通过网络结构产生。网络关联数据的分析需要考虑网络依赖性的统计推断工具和理论。所开发的方法将应用于压力和自杀研究的数据分析，帮助理解自杀行为背后的病理和生物学机制。主要研究者（PI）计划开发开源软件包，以传播的结果，并提供培训机会的研究生。第一部分的研究重点是开发方法和理论的回归系数和相关措施之间的推断两个变量的兴趣，当有网络依赖样本单位。在研究的第二部分，PI将专注于分析具有复制的网络链接数据。在一些应用中，可能存在多个独立的单元，并且每个单元内的观测到的多变量数据可能通过网络结构具有依赖性。这类网络依赖数据的分析由于其独立实现的可用性而呈现出其自身的特点。处理网络依赖性的挑战至少是双重的。第一个挑战是无限维，这可以通过网络邻域增长的概念来理解。第二个挑战是节点异质性，这意味着一般网络不具有欧氏格空间中的对称结构。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

Data with complex interpersonal dependency characterized by networks are increasingly encountered in many scientific areas. For example, in some survey studies for school students, a friendship network among students may also be collected in addition to traditional variables collected on each unit such as drug use, smoking and mental health status. The response of interest such as drug use is likely to have dependency across units through friendship networks. As another example, brain functional connectivity studies have consistently discovered functional linkage among brain regions, where dependency among brain regions arises through a network structure. The analysis of network-linked data calls for statistical inference tools and theories that consider network dependency. The developed methods will be applied to data analyses of stress and suicidal studies, helping understand the pathological and biological mechanisms underlying suicidal behaviors. The principal investigator (PI) plans to develop open-source software packages to disseminate the results and provide training opportunities for graduate students.The first part of the research focuses on developing methods and theory for the inference of regression coefficients and dependency measures between two variables of interest, when there is network dependency across sample units. In the second part of the research, the PI will focus on analyzing network-linked data with replicates. In some applications, multiple independent units may exist, and the observed multivariate data within each unit may have dependency through a network structure. The analysis of this type of network-dependent data exhibits its own features due to the availability of independent realizations. The challenges of dealing with network dependency are at least twofold. The first challenge is the infinite dimensionality, which can be understood through the notion of network neighborhood growth. The second challenge is node heterogeneity, which means a general network does not have the symmetric structure as in a Euclidean lattice space. This research will develop new statistical inference tools and theories addressing these challenges.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.