Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons
Vivek S. Borkar, Nikhil Karamchandani, Sharad Mirani

TL;DR
This paper introduces a randomized Kaczmarz algorithm for rank aggregation from pairwise comparisons under the BTL model, demonstrating theoretical convergence and empirical effectiveness in inferring overall rankings efficiently.
Contribution
The paper presents a novel application of the randomized Kaczmarz method to rank aggregation, with convergence analysis and practical algorithms for online and distributed settings.
Findings
Algorithm converges reliably under noisy data
Empirical results validate theoretical convergence rates
Method performs well in online and distributed environments
Abstract
We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as that of solving a noisy linear system, for which a ready algorithm is available in the form of the randomized Kaczmarz method. This scheme is provably convergent, has excellent empirical performance, and is amenable to on-line, distributed and asynchronous variants. Convergence, convergence rate, and error analysis of the proposed algorithm are presented and several numerical experiments are conducted whose results validate our theoretical findings.
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