Reviews: Covariate-Powered Empirical Bayes Estimation

The Authors provide a simple but powerful approach to empirical bayesian inference under rather broad assumptions. The method is relevant in settings where both a) standard statistical estimators (such as the average) can be evaluated and b) covariates can be used to train machine learning models to estimate the same value. The paper tries to solve this problem in the setting where the standard estimator is not reliable enough (e.g. because sample size is too small) and the covariates only give weak information on the target variable. The problem setting considered is highly relevant in many real-world settings. Considering the practical relevance and theoretical interest in empirical bayes methods, it seems quite surprising that this approach has not been investigated earlier (only for special cases such as linear models).