Generalized Top-k Mallows Model for Ranked Choices
Shahrzad Haddadan, Sara Ahmadian
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 top choices 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 generalized top-$k$ Mallows models, with a focus on analyzing buyer preferences and 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) a method for learning the model parameters from observed choice data. These contributions provide new tools for analysis and prediction in critical decision-making scenarios.We present  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.