Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons
Machine Learning
2016-05-10 v1 Machine Learning
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.
Cite
@article{arxiv.1605.02470,
title = {Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons},
author = {Vivek S. Borkar and Nikhil Karamchandani and Sharad Mirani},
journal= {arXiv preprint arXiv:1605.02470},
year = {2016}
}