Modeling Spin Configurations and Ranking

This project considers the modeling of ranking and categorical data that are strongly dependent in nature. Typical examples of dependent ranking data arise when one ranks students in a class based on exam scores, or when people rank movies on a website. Typical examples of dependent categorical data arise when one studies how the behavioral patterns of people in a social network (say smoking or voting preference) are influenced by their friends. Both types of data have become increasingly common. This project studies modeling schemes for such data aimed at capturing its dependence, which is not assumed to be well understood. The research develops a rigorous understanding of the behavior of these models, which will aid in statistical inferences from data sets of these types.

For the ranking work, the project will study the Mallows model of rankings and its generalizations. Most existing research concentrates on one particular such model, namely the Mallows model with Kendall's tau. This project instead puts forth a general framework based on permutation limit theory to understand the behavior of Mallows models and permutation models in general. For modeling dependent or categorical data, the focus is on Ising models, which originated in statistical physics and have received significant recent attention in statistics and machine learning. The main goal of the research is to develop inference for Ising model parameters that are not computationally prohibitive.