Ranking Inferences Based on Multiway Comparisons

Prof. Weichen WANG
Assistant Professor, the Hong Kong University

Date: 26 February 2024 (Monday)
Time: 10:30 am to 12:00 pm
Venue: E22-G015
Host: Prof. Yan LIN, Assistant Professor in Business Intelligence and Analytics


This paper considers ranking inference of n items based on the observed ranking results among multiple selected items at each trial. Two classical methods exist: the maximum likelihood estimator (MLE) and the spectral estimator. For the MLE, under a uniform sampling scheme in which any M distinguished items are selected for comparisons with probability p and the selected M items are compared L times with multinomial outcomes, we establish the statistical rates of convergence for the underlying n preference scores, with the minimum sampling complexity. For the spectral estimator, we can work with a very general and more realistic setup in which the comparison graph consists of hyper-edges of possible heterogeneous sizes and the number of comparisons can be as low as one for a given hyper-edge. In addition, we establish the asymptotic normality for both methods that allows us to construct confidence intervals for the underlying scores. We also unravel the relationship between the spectral estimator and the MLE. Given the asymptotic distributions of the estimated preference scores, we then introduce a novel framework to carry out both one-sample and two-sample inferences on ranks, applicable to both fixed and random graph settings. This comprehensive framework relies on a sophisticated maximum pairwise difference statistic whose distribution is estimated via a valid Gaussian multiplier bootstrap. Finally, we substantiate our findings with comprehensive numerical simulations and subsequently apply our developed methodologies to perform statistical inferences on statistics journals and movie rankings.



Prof. Weichen Wang joined The University of Hong Kong in 2021 as an Assistant Professor. He obtained his PhD in Operations Research and Financial Engineering from Princeton University in 2016. After graduation, he joined Two Sigma Investments as a quantitative researcher. Before his PhD, he received his bachelor’s degree in Mathematics and Physics from Tsinghua University in 2011. Prof. Wang’s research areas include big data analysis, econometrics, robust statistics and machine learning, and he is particularly interested in the factor structure of the financial market and real-world applications of machine learning. His works have been published in top journals including Annals of Statistics, Journal of Machine Learning Research, Journal of Econometrics, etc.

 All are welcome!