The classic Mallows model is a foundational tool for modeling user preferences. However, it has limitations in capturing real-world scenarios, where users often focus only on a limited set of preferred items and are indifferent to the rest. To address this, extensions such as the top-k Mallows model have been proposed, aligning better with practical applications. In this paper, we address several challenges related to the generalized top-k Mallows model, with a focus on analyzing buyer choices. Our key contributions are: (1) a novel sampling scheme tailored to generalized top-k Mallows models, (2) an efficient algorithm for computing choice probabilities under this model, and (3) an active learning algorithm for estimating the model parameters from observed choice data. These contributions provide new tools for analysis and prediction in critical decision-making scenarios. We present a rigorous mathematical analysis for the performance of our algorithms. Furthermore, through extensive experiments on synthetic data and real-world data, we demonstrate the scalability and accuracy of our proposed methods, and we compare the predictive power of Mallows model for top-k lists compared to the simpler Multinomial Logit model.

翻译：经典的Mallows模型是建模用户偏好的基础工具。然而，它在捕捉现实场景方面存在局限，因为用户通常只关注有限的偏好项目集，而对其余项目漠不关心。为解决此问题，已有诸如top-k Mallows模型等扩展被提出，这些扩展能更好地与实际应用相契合。本文针对广义化top-k Mallows模型相关的若干挑战展开研究，重点分析买家选择行为。我们的主要贡献包括：(1) 一种专为广义化top-k Mallows模型设计的新颖采样方案，(2) 一种在该模型下计算选择概率的高效算法，以及(3) 一种从观测选择数据中估计模型参数的主动学习算法。这些贡献为关键决策场景下的分析与预测提供了新工具。我们对所提算法的性能进行了严格的数学分析。此外，通过在合成数据和真实数据上进行大量实验，我们证明了所提方法的可扩展性和准确性，并比较了Mallows模型针对top-k列表的预测能力与更简单的多项Logit模型。