Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons

Vivek S. Borkar; Nikhil Karamchandani; Sharad Mirani

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arXiv · 1605.02470

Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons

Vivek S. Borkar·Nikhil Karamchandani·Sharad Mirani

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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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Vivek S. Borkar, Nikhil Karamchandani, Sharad Mirani. 2016-05-09. Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons. https://arxiv.org/abs/1605.02470

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