RI: Small: Modern Machine Learning Algorithms for Ranking from Pairwise and Higher-Order Comparisons

一次从几个项目之间的比较中对大量项目进行排名的问题在许多领域中起着至关重要的作用，包括推荐系统，众包，营销和计量经济学。在现代环境中，随着要排名的项目数量的增加以及相应数据集的大小和复杂性的增加，重新访问当前用于这些问题的经典算法并设计新算法至关重要，这些算法可以在更少的假设下更好地扩展到现代需求。该项目将为此类问题设计现代机器学习算法，同时培训博士生和博士后科学家，掌握为涉及现代数据集的问题设计新颖机器学习算法所需的跨学科技能。该项目的其他更广泛的影响还包括组织研讨会和/或教程，以传播在这里进行的研究结果，旨在向广大科学受众传达想法的调查文章，以及旨在增加代表性不足的群体参与STEM教育机会和职业的活动。两两比较的排序问题已经在几个领域进行了研究，包括统计学，运筹学，社会选择和计算机科学，并且已经开发了几种算法;然而，很少有人了解这些不同的算法如何相互关联，在什么条件下它们成功（或失败），以及如何从一个洞察力可以用来改进另一个。从高阶比较中排序的算法甚至更不容易理解。该项目将深入了解各种成对排名算法成功（或失败）的条件，并使用这种理解的见解来开发现代机器学习算法，这些算法具有强大的性能保证，可以从成对和高阶比较中进行排名。具体而言，该项目将研究以下三个方向：（1）了解当前算法成功或失败的成对模型条件。(2)设计新的机器学习算法，从成对比较中进行排名。(3)从高阶比较中进行排序。该项目将为从成对比较中进行排序的研究带来统一的视角，迄今为止，这种研究分散在不同的学科中;开发新的机器学习算法，改进各种排序目标的最新技术水平;并启动对高阶比较排名的系统研究，这是机器学习，统计学和计量经济学交叉的新兴领域。

The problem of ranking a large number of items from comparisons among a few items at a time plays a crucial role in many areas, including recommender systems, crowdsourcing, marketing, and econometrics. In modern settings, as the numbers of items to be ranked increase and corresponding datasets grow in size and complexity, it is critical to re-visit the classical algorithms currently used for these problems and to design new algorithms that can better scale to modern needs under fewer assumptions. This project will design modern machine learning algorithms for such problems, while training PhD students and postdoctoral scientists in the interdisciplinary skills needed to design novel machine learning algorithms for problems involving modern datasets. Other broader impacts of the project will also include organization of workshops and/or tutorials to disseminate the results of the research conducted here, survey articles aimed at conveying the ideas to a broad scientific audience, and activities designed to increase participation of under-represented groups in STEM education opportunities and careers. The problem of ranking from pairwise comparisons has been studied in several fields, including statistics, operations research, social choice, and computer science, and several algorithms have been developed; however, very little has been understood in terms of how these different algorithms relate to each other, under what conditions they succeed (or fail), and how insights from one can be used to improve another. Algorithms for ranking from higher-order comparisons are even less well understood. The project will develop a strong understanding of the conditions under which various pairwise ranking algorithms succeed (or fail), and use insights from this understanding to develop modern machine learning algorithms with strong performance guarantees for ranking from pairwise as well as higher-order comparisons. Specifically, the project will investigate the following three directions: (1) Understanding conditions on pairwise models under which current algorithms succeed or fail.(2) Design of new machine learning algorithms for ranking from pairwise comparisons.(3) Ranking from higher-order comparisons.The project will bring a unified perspective to the study of ranking from pairwise comparisons, which hitherto has been scattered across different disciplines; develop new machine learning algorithms that improve the state of the art for a variety of ranking objectives; and initiate a systematic study of ranking from higher-order comparisons, a nascent area at the intersection of machine learning, statistics and econometrics.