WORST-CASE VERSUS AVERAGE-CASE DESIGN FOR ESTIMATION FROM PARTIAL PAIRWISE COMPARISONS

• 成果类型: Article
• 署名作者: Pananjady, Ashwin; Mao, Cheng; Muthukumar, Vidya; Wainwright, Martin J.; Courtade, Thomas A.
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Berkeley; Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1838
• 发表日期: 2020
• 页码: 1072-1097
• 关键词: choice; models

摘要

Pairwise comparison data arises in many domains, including tournament rankings, web search and preference elicitation. Given noisy comparisons of a fixed subset of pairs of items, we study the problem of estimating the underlying comparison probabilities under the assumption of strong stochastic transitivity (SST). We also consider the noisy sorting subclass of the SST model. We show that when the assignment of items to the topology is arbitrary, these permutation-based models, unlike their parametric counterparts, do not admit consistent estimation for most comparison topologies used in practice. We then demonstrate that consistent estimation is possible when the assignment of items to the topology is randomized, thus establishing a dichotomy between worst-case and average-case designs. We propose two computationally efficient estimators in the average-case setting and analyze their risk, showing that it depends on the comparison topology only through the degree sequence of the topology. We also provide explicit classes of graphs for which the rates achieved by these estimators are optimal. Our results are corroborated by simulations on multiple comparison topologies.