Preference-Based Dynamic Ranking Structure Recognition
This work addresses the challenge of interpreting complex preference data for applications like recommendation systems, though it appears incremental as it builds on the Bradley-Terry model with temporal and structural enhancements.
The paper tackles the problem of uncovering hidden homogeneous structures in noisy preference-based data by introducing a dynamic ranking structure recognition framework, achieving consistency in ranking group recognition and demonstrating practical utility on synthetic and real-world datasets.
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.