Excellence in Research: Statistical Network Modeling and Inference for Complex Data

网络结构的估计和推断在基因组学、金融学等多个科学领域有着广泛的应用。然而，复杂数据的丰富对网络分析中新的统计学习方法提出了很大的需求。该项目的一个主要目标是开发一套新的方法和理论工具，以确定高维网络的变化点和推断结构变化。该项目的成功可能会对生物医学科学和金融产生重大影响。将数据应用于阿尔茨海默病和投资组合风险监测将有助于提供新的见解。该小组将开发计算程序包，以促进拟议方法的应用和向学术界和工业界传播。此外，研究将与教育紧密结合，通过联合监督学生和联合开发两所院校的课程。将招募代表人数不足的少数族裔学生，并参与该项目。该合作项目将为HBCU机构的学生和教职员工提供一个获得尖端研究和教育资源的机会，并有助于增加下一代数据科学家的多样性。该项目的研究有两个主要方向。第一个重点是异质数据的变点分析。为了检测高维图的可能变化点，在同时考虑所有节点的情况下，引入阈值变量和阈值参数，构造了一种高效的算法。为了同时识别高维线性模型中的变点，考虑了一种检验不同分段上相应回归系数的齐性的创新方法。对于第二个方向，发展了一种非参数检验方法来比较相关/协方差矩阵。该团队计划调查拟议方法的理论性质，并将这些方法应用于基因组学和金融学。该项目可以为统计学习和大数据文献提供独特的贡献。此外，从拟议的研究中获得的知识对于处理统计学和机器学习中的其他复杂的高维问题可能是有价值的。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Estimation and inference of network structure have wide applications in many scientific fields such as genomics and finance. However, the abundance of complex data presents a great demand for new statistical learning methods in network analysis. A main goal of this project is to develop a set of novel methodological and theoretical tools to identify change points and infer structural changes for high-dimensional networks. Success of this project can have significant impacts on biomedical sciences and finance. Data applications to the Alzheimer's disease and portfolio risk monitoring will help to offer new insights. The team will develop computational packages to facilitate the application and dissemination of the proposed methods to academia and industry. Furthermore, the research will be closely integrated with education, through joint supervision of students and joint development of courses from two institutions. Underrepresented minority students will be recruited and involved in the project. The collaborative project will provide an opportunity for students and faculty in an HBCU institution to gain access to cutting-edge research and educational resources, and help increase the diversity of the next generation of data scientists.The research of this project has two main directions. The first one focuses on change point analysis for heterogenous data. To detect possible change points of a high-dimensional graph, a threshold variable and a threshold parameter are introduced while considering all nodes simultaneously to construct a highly effective algorithm. To simultaneously identify change points in a high-dimensional linear model, an innovative method to test homogeneity of the corresponding regression coefficients across different segments is considered. For the second direction, a nonparametric testing method is developed to compare correlation/covariance matrices. The team plans to investigate theoretical properties of the proposed methods and apply the methods to genomics and finance. This project can provide unique contributions to the statistical learning and big data literature. In addition, the knowledge gained from the proposed research can be valuable for handling other complex high dimensional problems in statistics and machine learning.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.