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A0730
Title: Covariate-powered empirical Bayes estimation Authors:  Nikolaos Ignatiadis - Stanford University (United States) [presenting]
Stefan Wager - Stanford University (United States)
Abstract: Methods are studied for simultaneous analysis of many noisy experiments in the presence of rich covariate information. The goal of the analyst is to optimally estimate the true effect underlying each experiment. Both the noisy experimental results and the auxiliary covariates are useful for this purpose, but neither data source on its own captures all the information available to the analyst. We propose a flexible plug-in empirical Bayes estimator that synthesizes both sources of information and may leverage any black-box predictive model. We show that our approach is within a constant factor of minimax for a simple data-generating model. Furthermore, we establish an extension to the classic result of James-Stein, whereby our proposed estimator dominates the sample mean of the experimental results under quadratic risk; even if the auxiliary covariates contain no information about the true effects. Finally, we exhibit promising empirical performance of the method on both real and simulated data.