analiza aiqbench
This paper proposes a novel machine learning approach using isotonic regression to optimize the inverse link function in Bradley-Terry models, addressing common issues of model misspecification. By alternating between gradient-based parameter learning and monotonic improvement techniques, it enhances win probability predictions across sports datasets like football and tennis. The method offers practical improvements for ranking algorithms where strict ordering may be uncertain due to limited data.
Isotonic Bradley-Terry Model for Paired Comparison Data
arXiv:2608.02081v1 Announce Type: new Abstract: In this paper, we study prediction problems for paired comparison data, for example, predicting the win probability between two unmatched players and ranking all the players according to the order of their strengths by using win probability data between two matched players. Paired comparison data are typically analyzed using Bradley-Terry and Thurstone-Mosteller models. These models predict the win probability by transforming the difference between learned rate parameters, which represent players'\;strengths, with a pre-specified inverse link function, and employ the order of learned rate parameters for player ranking. However, these models may suffer from model misspecification owing to the selection of a fixed inverse link function. Therefore, in this study, we propose to learn the rate parameters by a (sub-)gradient method and the inverse link function by an isotonic regression technique alternately. The proposed model guarantees monotonic improvement in training error, and is likely to yield an exact tie when the available data is insufficient to establish a strict ranking. We also verified that the proposed model could improve the win probability prediction and ranking performance through numerical experiments with synthetic data and real-world data of football Premier League, baseball MLB, and tennis ATP tour.
Abstract:In this paper, we study prediction problems for paired comparison data, for example, predicting the win probability between two unmatched players and ranking all the players according to the order of their strengths by using win probability data between two matched players. Paired comparison data are typically analyzed using Bradley-Terry and Thurstone-Mosteller models. These models predict the win probability by transforming the difference between learned rate parameters, which represent players'\;strengths, with a pre-specified inverse link function, and employ the order of learned rate parameters for player ranking. However, these models may suffer from model misspecification owing to the selection of a fixed inverse link function. Therefore, in this study, we propose to learn the rate parameters by a (sub-)gradient method and the inverse link function by an isotonic regression technique alternately. The proposed model guarantees monotonic improvement in training error, and is likely to yield an exact tie when the available data is insufficient to establish a strict ranking. We also verified that the proposed model could improve the win probability prediction and ranking performance through numerical experiments with synthetic data and real-world data of football Premier League, baseball MLB, and tennis ATP tour.
Machine Learning (cs.LG)
arXiv:2608.02081 [cs.LG]
(or arXiv:2608.02081v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.02081 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 288 cuvinte
Subiecte conexe
[AINews] not much happened today
Latent Space · 3 oct. 2026
Covariate-dependent Joint Modeling of Multivariate Ordinal Preferences and Its Connections with Comparison Models
arXiv · 8 oct. 2026
When Can You Debias an LLM Judge? Identifiability Limits, a Test, and Designs for Top-k Ranking
arXiv · 21 iul. 2026
TuneJury: An Open Metric for Improving Music Generation Preference Alignment
arXiv · 16 iun. 2026