Generalized Top-k Mallows Model for Ranked Choices

2025-10-24

AI Summary

Classical Mallows models fail to capture realistic choice behaviors where users focus only on their top-$k$ preferences, inadequately representing partial preference and truncated choice settings. Method: We propose the generalized top-$k$ Mallows model, unifying partial and truncated preference modeling. We design an exact sampling algorithm based on rejection sampling, a dynamic programming algorithm for analytically computing selection probabilities of any item, and an active learning–based parameter estimation framework that substantially improves estimation accuracy and convergence speed under limited samples. Contributions/Results: Theoretical analysis establishes polynomial time complexity and statistical consistency of our algorithms. Experiments on synthetic and real-world datasets demonstrate that our model achieves significantly higher predictive accuracy than the Multinomial Logit model and existing top-$k$ Mallows variants, while offering strong interpretability, high scalability, and rigorous theoretical foundations.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Modeling user preferences with limited item focus
• Analyzing buyer choices under generalized top-k Mallows
• Computing choice probabilities and estimating model parameters

Innovation

• Novel sampling scheme for generalized top-k Mallows models
• Efficient algorithm computing choice probabilities under model
• Active learning algorithm estimating parameters from data