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Activity Number: 175 - Computational Methods for Complex Data Challenges
Type: Invited
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Computing
Abstract #320683
Title: Lagrangian Inference for Ranking Problems
Author(s): Ethan Fang* and Yue Liu and Junwei Lu
Companies: Duke University and Harvard University and Harvard University
Keywords: Ranking; Inference; Combinatorics; Bootstrap

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 proposed method aims to infer general ranking properties of the BTL model. 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 datasets to back up our theory.

Authors who are presenting talks have a * after their name.

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