# A General Pairwise Comparison Model for Extremely Sparse Networks

arXiv: https://arxiv.org/abs/2002.08853 · HTML: https://mlsanity.com/paper/2002.08853/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2020.

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

- [Statistical ranking with dynamic covariates](https://mlsanity.com/paper/2406.16507/) (2024)
- [Statistical inference for pairwise comparison models](https://mlsanity.com/paper/2401.08463/) (2024)
- [Minimax Hypothesis Testing for the Bradley-Terry-Luce Model](https://mlsanity.com/paper/2410.08360/) (2024)
- [A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency](https://mlsanity.com/paper/2211.09272/) (2022)
- [Convergence analysis of a family of Zermelo-type iterations for the Bradley--Terry model](https://mlsanity.com/paper/2607.22221/) (2026)
- [Random pairing MLE for estimation of item parameters in Rasch model](https://mlsanity.com/paper/2406.13989/) (2024)
- [Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications](https://mlsanity.com/paper/2501.07437/) (2025)
- [Bradley-Terry model under general comparison graphs](https://mlsanity.com/paper/2610.06237/) (2026)

## Abstract (arXiv)

Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample flexibility in terms of model parametrization. Under this setup, we show that the maximum likelihood estimator for the latent score vector of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This condition is sharp in terms of the leading order asymptotics describing the sparsity. Our analysis utilizes a novel chaining technique and illustrates an important connection between graph topology and model consistency. Our results guarantee that the maximum likelihood estimator is justified for estimation in large-scale pairwise comparison networks where data are asymptotically deficient. Simulation studies are provided in support of our theoretical findings.