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Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…

Methodology · Statistics 2026-01-13 Hisaya Okahara , Tomoyuki Nakagawa , Shonosuke Sugasawa

Aligning Large Language Models (LLMs) with human preferences is crucial in ensuring desirable and controllable model behaviors. Current methods, such as Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization…

Computation and Language · Computer Science 2025-10-24 Yang Zhao , Yixin Wang , Mingzhang Yin

Rankings derived from pairwise comparisons are central to many economic and computational systems. In the context of large language models (LLMs), rankings are typically constructed from human preference data and presented as leaderboards…

Computation and Language · Computer Science 2026-03-05 Angel Rodrigo Avelar Menendez , Yufeng Liu , Xiaowu Dai

A paired comparison analysis is the simplest way to make comparative judgments between objects where objects may be goods, services or skills. For a set of problems, this technique helps to choose the most important problem to solve first…

Methodology · Statistics 2020-02-27 Maqsood Ali , Muhammad Aslam

Evaluation in NLP is usually done by comparing the scores of competing systems independently averaged over a common set of test instances. In this work, we question the use of averages for aggregating evaluation scores into a final number…

Computation and Language · Computer Science 2021-10-22 Maxime Peyrard , Wei Zhao , Steffen Eger , Robert West

Pairwise preference learning is central to machine learning, with recent applications in aligning language models with human preferences. A typical dataset consists of triplets $(x, y^+, y^-)$, where response $y^+$ is preferred over…

Machine Learning · Computer Science 2026-02-12 Rattana Pukdee , Maria-Florina Balcan , Pradeep Ravikumar

We propose a general framework for statistical inference on the overall strengths of players in pairwise comparisons, allowing for potential shifts in the covariate distribution. These covariates capture important contextual information…

Methodology · Statistics 2025-04-10 Xiudi Li , Sijia Li

Pairwise comparison models have been widely used for utility evaluation and rank aggregation across various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the…

Statistics Theory · Mathematics 2025-12-16 Ruijian Han , Wenlu Tang , Yiming Xu

In this paper, we propose a listwise approach for constructing user-specific rankings in recommendation systems in a collaborative fashion. We contrast the listwise approach to previous pointwise and pairwise approaches, which are based on…

Machine Learning · Statistics 2019-02-08 Liwei Wu , Cho-Jui Hsieh , James Sharpnack

For nonbalanced paired comparisons, a wide variety of ranking methods have been proposed. One of the best popular methods is the Bradley-Terry model in which the ranking of a set of objects is decided by the maximum likelihood estimates…

Methodology · Statistics 2016-11-07 Ting Yan

Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…

Methodology · Statistics 2026-02-24 Lingfeng Lyu , Doudou Zhou

Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational…

Methodology · Statistics 2017-04-28 Valeria Vitelli , Øystein Sørensen , Marta Crispino , Arnoldo Frigessi , Elja Arjas

The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…

Optimization and Control · Mathematics 2022-03-29 Sally Giuseppe Arcidiacono , Salvatore Corrente , Salvatore Greco

Over the last few years, there has been a growing interest in the prediction and modelling of competitive sports outcomes, with particular emphasis placed on this area by the Bayesian statistics and machine learning communities. In this…

Applications · Statistics 2024-12-17 Roberto Macrì Demartino , Leonardo Egidi , Nicola Torelli

This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in…

Statistics Theory · Mathematics 2018-08-27 Sylvain Le Corff , Matthieu Lerasle , Elodie Vernet

Given pairwise comparisons between multiple items, how to rank them so that the ranking matches the observations? This problem, known as rank aggregation, has found many applications in sports, recommendation systems, and other web…

Machine Learning · Statistics 2023-09-12 Ziliang Samuel Zhong , Shuyang Ling

We describe the application of the Bradley-Terry model to NCAA Division I Men's Ice Hockey. A Bayesian construction gives a joint posterior probability distribution for the log-strength parameters, given a set of game results and a choice…

Applications · Statistics 2023-03-21 John T. Whelan , Adam Wodon

Data in the form of pairwise comparisons arises in many domains, including preference elicitation, sporting competitions, and peer grading among others. We consider parametric ordinal models for such pairwise comparison data involving a…

Bipartite ranking is a fundamental ranking problem that learns to order relevant instances ahead of irrelevant ones. The pair-wise approach for bi-partite ranking construct a quadratic number of pairs to solve the problem, which is…

Machine Learning · Computer Science 2017-08-25 Wei-Yuan Shen , Hsuan-Tien Lin

News recommendation is a challenging task that involves personalization based on the interaction history and preferences of each user. Recent works have leveraged the power of pretrained language models (PLMs) to directly rank news items by…

Information Retrieval · Computer Science 2024-09-27 Nithish Kannen , Yao Ma , Gerrit J. J. van den Burg , Jean Baptiste Faddoul
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