# Generalized Top-k Mallows Model for Ranked Choices

arXiv: https://arxiv.org/abs/2510.22040 · HTML: https://mlsanity.com/paper/2510.22040/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 37 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 10 of 10)

- [Efficiently Learning Mixtures of Mallows Models](https://mlsanity.com/paper/1808.05731/) (2018)
- [Concentric mixtures of Mallows models for top-k rankings: sampling and identifiability](https://mlsanity.com/paper/2010.14260/) (2020)
- [Learning Rich Rankings](https://mlsanity.com/paper/2312.15081/) (2023)
- [Learning Mixed Multinomial Logit Model from Ordinal Data](https://mlsanity.com/paper/1411.0073/) (2014)
- [Aggregating Incomplete and Noisy Rankings](https://mlsanity.com/paper/2011.00810/) (2020)
- [Robust Consensus in Ranking Data Analysis: Definitions, Properties and Computational Issues](https://mlsanity.com/paper/2303.12878/) (2023)
- [Statistical Models of Top-k Partial Orders](https://mlsanity.com/paper/2406.15893/) (2024)
- [Active Learning for Non-Parametric Choice Models](https://mlsanity.com/paper/2208.03346/) (2022)
- [Subset Selection Based On Multiple Rankings in the Presence of Bias: Effectiveness of Fairness Constraints for Multiwinner Voting Score Functions](https://mlsanity.com/paper/2306.09835/) (2023)
- [Fast Learning of MNL Model from General Partial Rankings with Application to Network Formation Modeling](https://mlsanity.com/paper/2112.15575/) (2021)

## Abstract (arXiv)

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.