Abstract

The Bradley-Terry-Luce (BTL) model is one of the most celebrated models for ranking inferences based on pairwise comparison data, which associates individuals with latent preference scores and produces ranks. An important question that arises is the uncertainty quantification for ranks. It is natural to think that ranks for two individuals are not trustworthy if there is only a subtle difference in their preference scores. In this paper, we explore the homogeneity of scores in the BTL model, which assumes that individuals cluster into groups with the same preference scores. We introduce the clustering algorithm in regression via data-driven segmentation (CARDS) penalty into the likelihood function, which can rigorously and automatically separate parameters and uncover group structure. Statistical properties of two versions of CARDS are analyzed. As a result, we achieve a faster convergence rate and sharper confidence intervals for the maximum likelihood estimation of preference scores, providing insight into the power of exploring low-dimensional structure in a high-dimensional setting. We analyze real data examples, including sports and journal ranking, to highlight the improved prediction performance and interpretation ability of our method.

About the speaker

Yuxin Tao is a fifth-year Ph.D. student in the Center for Statistical Science at Tsinghua University, advised by Professor Dong Li. Yuxin visited the Department of Statistics at Harvard University from 2022 to 2023, mentored by Professor Tracy Ke. Yuxin's primary research interests include financial econometrics, network analysis, ranking inference and topic modeling. Yuxin also conducts interdisciplinary research with experts in ecology and epidemiology. As a Ph.D. candidate, Yuxin's research has been published in the Journal of Econometrics, Statistica Sinica, and Proceedings of the National Academy of Sciences.