# Preference-Based Dynamic Ranking Structure Recognition

arXiv: https://arxiv.org/abs/2509.24493 · HTML: https://mlsanity.com/paper/2509.24493/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Builds on (most cited first, 14 of 14)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisons](https://mlsanity.com/paper/2301.11270/) (2023)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Provable Pluralistic Alignment: Multi-Party RLHF under Offline Human Feedback](https://mlsanity.com/paper/2403.05006/) (2024)
- [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)
- [sparsegl: An R Package for Estimating Sparse Group Lasso](https://mlsanity.com/paper/2208.02942/) (2022)
- [Nonparametric Estimation in the Dynamic Bradley-Terry Model](https://mlsanity.com/paper/2003.00083/) (2020)
- [Contextual Online Uncertainty-Aware Preference Learning for Human Feedback](https://mlsanity.com/paper/2504.19342/) (2025)
- [Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method](https://mlsanity.com/paper/2109.13743/) (2021)
- [CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration](https://mlsanity.com/paper/1606.05158/) (2016)
- [Detecting Abrupt Changes in Sequential Pairwise Comparison Data](https://mlsanity.com/paper/2205.12431/) (2022)
- [A Spectral Approach for the Dynamic Bradley-Terry Model](https://mlsanity.com/paper/2307.16642/) (2023)

## Abstract (arXiv)

Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to identify dynamic ranking groups by incorporating temporal penalties into a spectral estimation for the celebrated Bradley-Terry model. To detect structural changes, we introduce an innovative objective function and present a practicable algorithm based on dynamic programming. Theoretically, we establish the consistency of ranking group recognition by exploiting properties of a random `design matrix' induced by a reversible Markov chain. We also tailor a group inverse technique to quantify the uncertainty in item ability estimates. Additionally, we prove the consistency of structure change recognition, ensuring the robustness of the proposed framework. Experiments on both synthetic and real-world datasets demonstrate the practical utility and interpretability of our approach.