Simple, Robust and Optimal Ranking from Pairwise Comparisons. (arXiv:1512.08949v1 [cs.LG])

We consider data in the form of pairwise comparisons of n items, with the goal of precisely identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items. We consider a simple counting algorithm that ranks the items in order of the number of pairwise comparisons won, and show it has three important and useful features: (a) Computational efficiency: the simplicity of the method leads to speed-ups of several orders of magnitude in computation time as compared to prior work; (b) Robustness: our theoretical guarantees make no assumptions on the pairwise-comparison probabilities, while prior work is restricted to the specific BTL model and performs poorly if the data is not true to it; and (c) Optimality: we show that up to constant factors, our algorithm achieves the information-theoretic limits for recovering the top-k subset. Finally, we extend our results to obtain sharp guarantees for approximate recovery under the Hamming distortion metric.

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