Statistical Investigations in Ranking from Pairwise and Multi-wise Comparisons

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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.