# Concentric mixtures of Mallows models for top-k rankings: sampling and identifiability

arXiv: https://arxiv.org/abs/2010.14260 · HTML: https://mlsanity.com/paper/2010.14260/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2020.

## Built on by (most cited first, 8 of 8)

- [Unsupervised Model Selection for Time-series Anomaly Detection](https://mlsanity.com/paper/2210.01078/) (2022)
- [Statistical Depth Functions for Ranking Distributions: Definitions, Statistical Learning and Applications](https://mlsanity.com/paper/2201.08105/) (2022)
- [On A Mallows-type Model For (Ranked) Choices](https://mlsanity.com/paper/2207.01783/) (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)
- [Who Pays the RENT? Implications of Spatial Inequality for Prediction-Based Allocation Policies](https://mlsanity.com/paper/2508.08573/) (2025)
- [Federated Aggregation of Mallows Rankings: A Comparative Analysis of Borda and Lehmer Coding](https://mlsanity.com/paper/2409.00848/) (2024)
- [Surprisingly Popular Voting for Concentric Rank-Order Models](https://mlsanity.com/paper/2411.08367/) (2024)
- [Generalized Top-k Mallows Model for Ranked Choices](https://mlsanity.com/paper/2510.22040/) (2025)

## Abstract (arXiv)

In this paper, we consider mixtures of two Mallows models for top-k rankings, both with the same location parameter but with different scale parameters, i.e., a mixture of concentric Mallows models. This situation arises when we have a heterogeneous population of voters formed by two homogeneous populations, one of which is a subpopulation of expert voters while the other includes the non-expert voters. We propose efficient sampling algorithms for Mallows top-k rankings. We show the identifiability of both components, and the learnability of their respective parameters in this setting by, first, bounding the sample complexity for the Borda algorithm with top-k rankings and second, proposing polynomial time algorithm for the separation of the rankings in each component. Finally, since the rank aggregation will suffer from a large amount of noise introduced by the non-expert voters, we adapt the Borda algorithm to be able to recover the ground truth consensus ranking which is especially consistent with the expert rankings.