Lagrangian Inference for Ranking Problems

• 成果类型: Article
• 署名作者: Liu, Yue; Fang, Ethan X.; Lu, Junwei
• 署名单位: Harvard University; Duke University; Harvard University; Harvard T.H. Chan School of Public Health
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2313
• 发表日期: 2023
• 页码: 202-223
• 关键词: false discovery rate; confidence-regions; likelihood ratio; inequality constraints; pairwise comparisons; aggregation; tests; regression; bootstrap; intervals

摘要

We propose a novel combinatorial inference framework to conduct general uncertainty quantification in ranking problems. We consider the widely adopted Bradley-Terry-Luce (BTL) model, where each item is assigned a positive preference score that determines the Bernoulli distributions of pairwise comparisons' outcomes. Our proposedmethod aims to infer general ranking properties of the BTLmodel. The general ranking properties include the local properties such as if an item is preferred over another and the global properties such as if an item is among the top K-ranked items. We further generalize our inferential framework to multiple testing problems where we control the false discovery rate (FDR) and apply the method to infer the top-K ranked items. We also derive the information-theoretic lower bound to justify the minimax optimality of the proposed method. We conduct extensive numerical studies using both synthetic and real data sets to back up our theory.