# Estimation of partial rankings from sparse, noisy comparisons

arXiv: https://arxiv.org/abs/2501.02505 · HTML: https://mlsanity.com/paper/2501.02505/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 84 references that are in the map.
- First posted on arXiv 5 Jan 2025.

## Builds on (most cited first, 18 of 18)

- [Efficient computation of rankings from pairwise comparisons](https://mlsanity.com/paper/2207.00076/) (2022)
- [Bayesian stochastic blockmodeling](https://mlsanity.com/paper/1705.10225/) (2017)
- [Nonparametric Bayesian inference of the microcanonical stochastic block model](https://mlsanity.com/paper/1610.02703/) (2016)
- [A physical model for efficient ranking in networks](https://mlsanity.com/paper/1709.09002/) (2017)
- [Revealing consensus and dissensus between network partitions](https://mlsanity.com/paper/2005.13977/) (2020)
- [Luck, skill, and depth of competition in games and social hierarchies](https://mlsanity.com/paper/2312.04711/) (2023)
- [Statistical Modelling of Citation Exchange Between Statistics Journals](https://mlsanity.com/paper/1312.1794/) (2013)
- [Belief propagation for permutations, rankings, and partial orders](https://mlsanity.com/paper/2110.00513/) (2021)
- [Spatial regionalization based on optimal information compression](https://mlsanity.com/paper/2111.01813/) (2021)
- [Inference of dynamic hypergraph representations in temporal interaction data](https://mlsanity.com/paper/2308.16546/) (2023)
- [Efficient method for estimating the number of communities in a network](https://mlsanity.com/paper/1706.02324/) (2017)
- [Efficient and Accurate Learning of Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/2302.05343/) (2023)
- [The interplay between ranking and communities in networks](https://mlsanity.com/paper/2112.12670/) (2021)
- [Ordered community detection in directed networks](https://mlsanity.com/paper/2203.16460/) (2022)
- [Joint Learning from Heterogeneous Rank Data](https://mlsanity.com/paper/2407.10846/) (2024)
- [Ranking in the generalized Bradley-Terry models when the strong connection condition fails](https://mlsanity.com/paper/1411.1168/) (2014)
- [A model for efficient dynamical ranking in networks](https://mlsanity.com/paper/2307.13544/) (2023)
- [Bayesian Rank-Clustering](https://mlsanity.com/paper/2406.19563/) (2024)

## Built on by (most cited first, 3 of 3)

- [Human-AI Collaborative Autonomous Experimentation With Proxy Modeling for Comparative Observation](https://mlsanity.com/paper/2603.12618/) (2026)
- [New insights into Elo algorithm for practitioners and statisticians](https://mlsanity.com/paper/2604.03840/) (2026)
- [Scalable inference of spatial regions and temporal signatures from time series](https://mlsanity.com/paper/2605.05008/) (2026)

## Abstract (arXiv)

Ranking items based on pairwise comparisons is common, from using match outcomes to rank sports teams to using purchase or survey data to rank consumer products. Statistical inference-based methods such as the Bradley-Terry model, which extract rankings based on an underlying generative model, have emerged as flexible and powerful tools to tackle ranking in empirical data. In situations with limited and/or noisy comparisons, it is often challenging to confidently distinguish the performance of different items based on the evidence available in the data. However, most inference-based ranking methods choose to assign each item to a unique rank or score, suggesting a meaningful distinction when there is none. Here, we develop a principled nonparametric Bayesian method, adaptable to any statistical ranking method, for learning partial rankings (rankings with ties) that distinguishes among the ranks of different items only when there is sufficient evidence available in the data. We develop a fast agglomerative algorithm to perform Maximum A Posteriori (MAP) inference of partial rankings under our framework and examine the performance of our method on a variety of real and synthetic network datasets, finding that it frequently gives a more parsimonious summary of the data than traditional ranking, particularly when observations are sparse.