Statistical Inference for Exchangeable Network Models

In recent years, there has been a tremendous surge in the availability of relational data in various scientific fields. For example, in biology, an abundance of data has been collected from metabolic networks, gene regulatory networks, brain networks, and ecological networks. Consequently, there is substantial interest from the scientific community in principled statistical procedures for drawing inferences from such array data. This project will develop broadly applicable statistical tools for such problems, enabling reliable inference across a range of applications, and will provide research training opportunities for graduate students. This project has three research aims. The first aim is to develop uncertainty quantification methods for array prediction problems that offer rigorous theoretical guarantees even when complex forms of missingness are present. The second aim is to develop an assumption-lean inference framework for regression problems involving network-linked data. The third aim of the project is to develop variants of the permutation test in various two-sample problems involving network data. Across all subproblems, we work under the framework of a jointly exchangeable array, which encompasses a vast range of data-generating processes and ensures that the developed methods will be widely applicable across different scientific 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.