Preference-Based Dynamic Ranking Structure Recognition

2025-09-29

AI Summary

This paper addresses the problem of identifying latent dynamic ranking structures—specifically, time-varying groupings and structural change points—in preference data. Methodologically, it extends the Bradley–Terry model to capture time-varying ability parameters with grouped dynamics; formulates a dynamic programming–based objective for structural change detection; and establishes a theoretical framework for the randomness of the design matrix derived from reversible Markov chains, introducing the group inverse technique—novel in this context—to quantify estimation uncertainty of ability parameters. By jointly optimizing spectral estimation, temporal regularization, and group inverse analysis, the framework consistently identifies both dynamic ranking groupings and structural breakpoints. Experiments on synthetic and real-world datasets demonstrate that the method achieves high robustness, statistical consistency, and interpretability.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Identifying dynamic ranking groups in preference-based data
• Detecting structural changes with innovative objective functions
• Establishing theoretical consistency for ranking recognition robustness

Innovation

• Incorporates temporal penalties into Bradley-Terry spectral estimation
• Uses dynamic programming algorithm for structural change detection
• Applies group inverse technique for uncertainty quantification