Covariate-Powered Empirical Bayes Estimation
This method addresses the challenge of synthesizing multiple data sources for more accurate effect estimation in statistical analysis, representing an incremental improvement with theoretical guarantees.
The paper tackles the problem of estimating true effects from many noisy experiments using both experimental results and auxiliary covariates, proposing a flexible plug-in empirical Bayes estimator that achieves constant-factor minimax optimality and robust convergence guarantees.
We study methods 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. In this paper, 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 robust convergence guarantees for our method that hold under considerable generality, and exhibit promising empirical performance on both real and simulated data.