The Isotonic Mechanism for Exponential Family Estimation
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In 2023, the International Conference on Machine Learning (ICML) required authors with multiple submissions to rank their submissions based on perceived quality. In this paper, we aim to employ these author-specified rankings to enhance peer review in machine learning and artificial intelligence conferences by extending the Isotonic Mechanism (Su, 2021, 2022) to exponential family distributions. This mechanism generates adjusted scores closely align with the original scores while adhering to author-specified rankings. Despite its applicability to a broad spectrum of exponential family distributions, this mechanism's implementation does not necessitate knowledge of the specific distribution form. We demonstrate that an author is incentivized to provide accurate rankings when her utility takes the form of a convex additive function of the adjusted review scores. For a certain subclass of exponential family distributions, we prove that the author reports truthfully only if the question involves only pairwise comparisons between her submissions, thus indicating the optimality of ranking in truthful information elicitation. Lastly, we show that the adjusted scores improve dramatically the accuracy of the original scores and achieve nearly minimax optimality for estimating the true scores with statistical consistecy when true scores have bounded total variation.
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