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

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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.