Collaborative Research: Inference for Networks: Bridging the Gap between Metric Spaces and Graphs

网络数据代表了单元之间的交互和关系，在许多科学学科和技术领域已经变得无处不在。分析如此复杂和结构新颖的数据需要超越传统统计学范围的新思想和工具。将开发一系列方法用于涉及网络数据的几种常见统计分析，这些分析的动机是网络安全，社会行为研究，遗传学和医学成像中的各种应用问题。这些方法可用于识别复杂系统可靠性的风险因素，推断社会和同伴对健康相关行为的影响，灵活地对基因之间的差异网络进行建模，并从大脑图像中推断神经元功能。研究结果将通过出版物和演讲传播，但也将纳入教学。该研究将包括适合学生参与各级项目，并强调本科生的研究培训。这些代码将通过以R编程语言执行的统计程序包提供，以供更广泛使用。该研究的主题是通过将度量空间中成熟的统计方法连接和扩展到网络数据来开发通用和灵活的网络分析工具。总体而言，开发这些工具的技术挑战包括缺乏明确的采样单位和样本大小定义，以及网络观测的离散性和噪声性。应对这些挑战需要扩展和组合来自不同研究领域的工具，包括随机矩阵理论，优化算法和统计推断。PI与计算机科学、社会科学和医学科学的研究人员之间的合作将为将开发的方法应用于这些领域的现实问题提供机会。该奖项反映了NSF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。

Network data, representing interactions and relationships between units, has become ubiquitous in many science disciplines and technology areas. Analyzing such complex and structurally novel data requires new ideas and tools beyond the scope of classical statistics. A sequence of methods will be developed for several common statistical analyses involving network data, motivated by various applied problems in cyber-security, social behavior studies, genetics, and medical imaging. These methods can be used to identify the risk factors for the reliability of a complex system, to infer social and peer effects on health-related behaviors, to flexibly model the differential networks between genes, and to infer neuron functionality from brain images. The results will be disseminated through publications and presentations, but will also be incorporated in teaching. The research will include projects suitable for student participation at various levels, and undergraduate research training will be emphasized. The codes will be provided through statistical packages implemented in the programming language R for broader use. The broad theme of the research is developing versatile and flexible network analysis tools by connecting and extending mature statistical methods in metric space to network data. Overall, the technical challenges in developing these tools range from the lack of clear definitions for sampling units and sample sizes, to the discrete and noisy nature of network observations. Addressing such challenges requires extensions and combinations of tools from different research areas, including random matrix theory, optimization algorithms, and statistical inference. Collaborations between the PI and researchers in computer science, social science, and medical sciences will provide opportunities to apply the developed methods to real-world problems in these domains.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.