Stretching the Effectiveness of MLE from Accuracy to Bias for Pairwise Comparisons
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Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:6676, 2020.
Abstract
A number of applications (e.g., AI bot tournaments, sports, peer grading, crowdsourcing) use pairwise comparison data and the BradleyTerryLuce (BTL) model to evaluate a given collection of items (e.g., bots, teams, students, search results). Past work has shown that under the BTL model, the widelyused maximumlikelihood estimator (MLE) is minimaxoptimal in estimating the item parameters, in terms of the mean squared error. However, another important desideratum for designing estimators is fairness. In this work, we consider one specific type of fairness, which is the notion of bias in statistics. We show that the MLE incurs a suboptimal rate in terms of bias. We then propose a simple modification to the MLE, which "stretches" the bounding box of the maximumlikelihood optimizer by a small constant factor from the underlying ground truth domain. We show that this simple modification leads to an improved rate in bias, while maintaining minimaxoptimality in the mean squared error. In this manner, our proposed class of estimators provably improves fairness in the sense of bias without loss in accuracy.
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