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Iterative ranking from pair-wise comparisons
Sahand N Negahban · Sewoong Oh · Devavrat Shah

Wed Dec 05 03:34 PM -- 03:38 PM (PST) @ Harveys Convention Center Floor, CC

The question of aggregating pairwise comparisons to obtain a global ranking over a collection of objects has been of interest for a very long time: be it ranking of online gamers (e.g. MSR’s TrueSkill system) and chess players, aggregating social opinions, or deciding which product to sell based on transactions. In most settings, in addition to obtaining ranking, finding ‘scores’ for each object (e.g. player’s rating) is of interest to understanding the intensity of the preferences. In this paper, we propose a novel iterative rank aggregation algorithm for discovering scores for objects from pairwise comparisons. The algorithm has a natural random walk interpretation over the graph of objects with edges present between two objects if they are compared; the scores turn out to be the stationary probability of this random walk. The algorithm is model independent. To establish the efficacy of our method, however, we consider the popular Bradley-Terry-Luce (BTL) model in which each object has an associated score which determines the probabilistic outcomes of pairwise comparisons between objects. We bound the finite sample error rates between the scores assumed by the BTL model and those estimated by our algorithm. This, in essence, leads to order-optimal dependence on the number of samples required to learn the scores well by our algorithm. Indeed, the experimental evaluation shows that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms a recently proposed algorithm by Ammar and Shah [1].

Author Information

Sahand N Negahban (University of California, Berkeley)
Sewoong Oh (University of Washington)
Devavrat Shah (Massachusetts Institute of Technology)

Devavrat Shah is a professor of Electrical Engineering & Computer Science and Director of Statistics and Data Science at MIT. He received PhD in Computer Science from Stanford. He received Erlang Prize from Applied Probability Society of INFORMS in 2010 and NeuIPS best paper award in 2008.

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