Modeling and Inference for Data with Network Dependency

具有网络依赖性的数据的建模和推理

• 批准号: 2210402
• 负责人: Kehui Chen
• 金额: $ 15万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210402&HistoricalAwards=false
• 关键词: Modeling; Inference; Data; Network; Dependency

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.

在许多科学领域，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，除了在每个单元上收集药物使用、吸烟和心理健康状况等传统变量外，还可以收集学生之间的友谊网络。诸如吸毒之类的兴趣反应很可能通过友谊网络在各个单位之间产生依赖。另一个例子是，脑功能连通性研究不断发现脑区域之间的功能联系，其中脑区域之间的依赖是通过网络结构产生的。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。首席研究员（PI）计划开发开源软件包来传播结果并为研究生提供培训机会。研究的第一部分侧重于开发方法和理论，用于在样本单元之间存在网络依赖的情况下推断两个感兴趣的变量之间的回归系数和依赖度量。在研究的第二部分，PI将重点分析具有复制的网络链接数据。在某些应用中，可能存在多个独立的单元，并且每个单元中观察到的多变量数据可能通过网络结构具有依赖性。由于独立实现的可用性，对这类依赖于网络的数据的分析显示出其自身的特点。处理网络依赖的挑战至少是双重的。第一个挑战是无限维度，这可以通过网络邻域增长的概念来理解。第二个挑战是节点的异构性，这意味着一般网络不像欧几里得晶格空间那样具有对称结构。这项研究将开发新的统计推断工具和理论来解决这些挑战。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。