# Hypothesis Testing for Generalized Thurstone Models

arXiv: https://arxiv.org/abs/2512.02912 · HTML: https://mlsanity.com/paper/2512.02912/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 71 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence](https://mlsanity.com/paper/1505.01462/) (2015)
- [Spectral Method and Regularized MLE Are Both Optimal for Top-K Ranking](https://mlsanity.com/paper/1707.09971/) (2017)
- [Uncertainty quantification in the Bradley-Terry-Luce model](https://mlsanity.com/paper/2110.03874/) (2021)
- [Lagrangian Inference for Ranking Problems](https://mlsanity.com/paper/2110.00151/) (2021)
- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [Uncertainty Quantification of MLE for Entity Ranking with Covariates](https://mlsanity.com/paper/2212.09961/) (2022)
- [On kernel methods for covariates that are rankings](https://mlsanity.com/paper/1603.08035/) (2016)
- [Nonparametric Estimation in the Dynamic Bradley-Terry Model](https://mlsanity.com/paper/2003.00083/) (2020)
- [Learning Rich Rankings](https://mlsanity.com/paper/2312.15081/) (2023)
- [Fundamental Limits of Testing the Independence of Irrelevant Alternatives in Discrete Choice](https://mlsanity.com/paper/2001.07042/) (2020)
- [Two-Sample Testing on Ranked Preference Data and the Role of Modeling Assumptions](https://mlsanity.com/paper/2006.11909/) (2020)
- [Statistical inference for pairwise comparison models](https://mlsanity.com/paper/2401.08463/) (2024)
- [Minimax Hypothesis Testing for the Bradley-Terry-Luce Model](https://mlsanity.com/paper/2410.08360/) (2024)
- [Estimation of Skill Distributions](https://mlsanity.com/paper/2006.08189/) (2020)

## Built on by (most cited first, 1 of 1)

- [Entrywise Error Bounds for Spectral Ranking with Semi-Random Adversaries](https://mlsanity.com/paper/2605.23854/) (2026)

## Abstract (arXiv)

In this work, we develop a hypothesis testing framework to determine whether pairwise comparison data is generated by an underlying generalized Thurstone model TF for a given choice function F. While prior work has predominantly focused on parameter estimation and uncertainty quantification for such models, we address the fundamental problem of minimax hypothesis testing for TF models. We formulate this testing problem by introducing a notion of separation distance between general pairwise comparison models and the class of TF models. We then derive upper and lower bounds on the critical threshold for testing that depend on the topology of the observation graph. For the special case of complete observation graphs, this threshold scales as Theta((nk)-1/2), where n is the number of agents and k is the number of comparisons per pair. Furthermore, we propose a hypothesis test based on our separation distance, construct confidence intervals, establish time-uniform bounds on the probabilities of type I and II errors using reverse martingale techniques, and derive minimax lower bounds using information-theoretic methods. Finally, we validate our results through experiments on synthetic and real-world datasets.