Statistical Investigations in Ranking from Pairwise and Multi-wise Comparisons

成对和多重比较排名的统计调查

• 批准号: 2112988
• 负责人: Ye Zhang
• 金额: $ 22万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2112988&HistoricalAwards=false
• 关键词: Statistical; Investigations; Ranking; Pairwise; Multi

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.

在广泛的学习和社会背景下，通过比较进行排名是一个核心问题。包括心理学、经济学和计算机科学在内的各个学科的研究人员都对排名问题做出了重大贡献。尽管取得了很大进展，但许多具有根本重要性的统计任务仍不明确。一个例子出现在量化排名过程的不确定性和分析多明智的比较数据，这自然出现在推荐系统，网络搜索，社会选择和许多其他领域。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在实现目标方面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推动包括统计、优化和机器学习在内的广泛领域之间的相互作用。新的课程将结合项目的成果开发，研究生也将通过他们在PI监督下的研究工作参与项目。该项目侧重于以下两个方向。首先，PI将量化成对比较中排名的不确定性。为了实现这一目标，PI将进行彻底的细粒度和条目统计调查。其次，PI将通过调查各种任务，包括开发最佳程序，进行入口分析等，加深对多方面比较的理论和方法论理解。沿着这些方向的进展将朝着奠定坚实的理论基础的目标，反馈到实际方法的发展和知情的应用程序的排名问题。这个奖项反映了NSF的法定使命，并已被认为是值得通过评估使用基金会的智力价值和更广泛的影响审查标准的支持。

项目成果

Partial recovery for top-k ranking: Optimality of MLE and SubOptimality of the spectral method

top-k 排序的部分恢复：MLE 的最优性和谱方法的次最优性

• DOI: 10.1214/21-aos2166
• 发表时间: 2022
• 期刊: The Annals of Statistics
• 作者: Chen, Pinhan;Gao, Chao;Zhang, Anderson Y.
• 通讯作者: Zhang, Anderson Y.

Optimal and Private Learning from Human Response Data

从人类反应数据中进行最佳和私人学习

• 发表时间: 2023
• 期刊: Proceedings of The 26th International Conference on Artificial Intelligence and Statistics
• 作者: Nguyen, Duc;Zhang, Anderson Ye
• 通讯作者: Zhang, Anderson Ye

A Spectral Approach to Item Response Theory

项目反应理论的谱方法

• 发表时间: 2022
• 期刊: Advances in neural information processing systems
• 作者: Nguyen, Duc;Zhang, Anderson
• 通讯作者: Zhang, Anderson

Uncertainty quantification in the Bradley–Terry–Luce model

Bradley–Terry–Luce 模型中的不确定性量化

• DOI: 10.1093/imaiai/iaac032
• 发表时间: 2023
• 期刊: Information and Inference: A Journal of the IMA
• 作者: Gao, Chao;Shen, Yandi;Zhang, Anderson Y.
• 通讯作者: Zhang, Anderson Y.

Optimal full ranking from pairwise comparisons

成对比较的最佳完整排名

• DOI: 10.1214/22-aos2175
• 发表时间: 2022
• 期刊: The Annals of Statistics
• 作者: Chen, Pinhan;Gao, Chao;Zhang, Anderson Y.
• 通讯作者: Zhang, Anderson Y.