THE ASYMPTOTICS OF RANKING ALGORITHMS

• 成果类型: Article
• 署名作者: Duchi, John C.; Mackey, Lester; Jordan, Michael I.
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Berkeley; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1142
• 发表日期: 2013
• 页码: 2292-2323
• 关键词: statistical-analysis; decision-making; minus 2; CLASSIFICATION; capacity; online; plus

摘要

We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this setting, these procedures require that individuals provide a complete ranking of all items, which is rarely feasible in practice. Instead, individuals routinely provide partial preference information, such as pairwise comparisons of items, and more practical approaches to ranking have aimed at modeling this partial preference data directly. As we show, however, such an approach raises serious theoretical challenges. Indeed, we demonstrate that many commonly used surrogate losses for pairwise comparison data do not yield consistency; surprisingly, we show inconsistency even in low-noise settings. With these negative results as motivation, we present a new approach to supervised ranking based on aggregation of partial preferences, and we develop U-statistic-based empirical risk minimization procedures. We present an asymptotic analysis of these new procedures, showing that they yield consistency results that parallel those available for classification. We complement our theoretical results with an experiment studying the new procedures in a large-scale web-ranking task.