通过动态排名分组识别复杂偏好数据中的隐藏结构。
Preference-Based Dynamic Ranking Structure Recognition
- 基于谱估计与时间惩罚，识别随时间变化的排名群体。
- 提出新目标函数与动态规划算法，准确检测结构变化。
- 理论保证一致性，适合有时间序列偏好的数据分析。
偏好数据常呈现复杂且嘈杂的特征，但可能隐藏着潜在的同质结构。本文提出一种新的偏好数据排名结构识别框架。首先，通过在著名的Bradley-Terry模型的谱估计中引入时间惩罚项，实现动态排名群体的识别。为检测结构变化，设计了一种创新的目标函数，并提出了基于动态规划的可行算法。理论上，利用由可逆马尔可夫链诱导的随机‘设计矩阵’的性质，建立了排名群体识别的一致性。此外，还引入群逆技术以量化项目能力估计的不确定性。同时证明了结构变化识别的一致性，确保了所提框架的鲁棒性。在合成与真实世界数据集上的实验验证了该方法的实用性和可解释性。
原文摘要 · Abstract (English)
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.
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