Statistical Investigations in Ranking from Pairwise and Multi-wise Comparisons

在广泛的学习和社会背景下，通过比较进行排名是一个中心问题。心理学、经济学和计算机科学等多个学科的研究人员对排名问题做出了重大贡献。尽管取得了很大进展，但许多根本性的重要统计任务仍不明朗。一个例子出现在量化排名过程的不确定性和分析多方面的比较数据，这在推荐系统、网络搜索、社交选择和许多其他领域中自然出现。该项目旨在通过系统的统计和计算调查，深入了解排名问题，以应对这些挑战。排名问题的广泛重要应用确保了我们朝着我们的目标取得的进展将对广泛的科学界产生重大影响。开发的技术和方法将进一步促进统计、优化和机器学习等广泛领域之间的相互作用。将结合该项目的成果开发新的课程，研究生也将通过他们在PPI监督下的研究工作参与该项目。该项目侧重于以下两个方向。首先，PI将从成对比较中量化排名的不确定性。为了实现这一目标，PI将进行彻底的细粒度和逐项统计调查。其次，PI将通过调查各种任务，包括制定最佳程序、进行条目分析等，加深对多层次比较的理论和方法的理解。沿着这些方向的进展将朝着奠定坚实的理论基础的目标前进，该基础反馈到对问题进行排名的实用方法和知情应用的发展。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Ranking from comparisons is a central problem in a wide range of learning and social contexts. Researchers in various disciplines including psychology, economics, and computer science have made significant contributions to the ranking problem. Despite much progress, many fundamentally important statistical tasks remain unclear. One example arises in quantifying the uncertainty of ranking procedures and in analyzing multi-wise comparison data, which appears naturally in recommendation systems, web search, social choice, and many other areas. This project aims to address these challenges by developing an in-depth understanding of the ranking problem through a systematic statistical and computational investigation. The wide range of important applications of the ranking problem ensures that the progress we make towards our objectives will have a great impact on a broad scientific community. The techniques and methods developed will further advance the interplay between a wide range of areas including statistics, optimization, and machine learning. New courses will be developed incorporating results from the project and graduate students will also be involved in the project through their research work supervised by the PI.This project focuses on the following two directions. First, the PI will quantify the uncertainty in ranking from pairwise comparisons. To achieve this goal, the PI will carry out a thorough fine-grained and entrywise statistical investigation. Second, the PI will deepen theoretical and methodological understanding of the multi-wise comparisons by investigating various tasks including developing optimal procedures, carrying out entrywise analysis, and others. Advances along these directions will be made towards the goal of laying out a firm theoretic foundation that feeds back into the development of practical methodology and informed applications for ranking problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.