  We propose a new empirical Bayes method for covariate-assisted multiple
testing with false discovery rate (FDR) control, where we model the local false
discovery rate for each hypothesis as a function of both its covariates and
p-value. Our method refines the adaptive p-value thresholding (AdaPT) procedure
by generalizing its masking scheme to reduce the bias and variance of its false
discovery proportion estimator, improving the power when the rejection set is
small or some null p-values concentrate near 1. We also introduce a Gaussian
mixture model for the conditional distribution of the test statistics given
covariates, modeling the mixing proportions with a generic user-specified
classifier, which we implement using a two-layer neural network. Like AdaPT,
our method provably controls the FDR in finite samples even if the classifier
or the Gaussian mixture model is misspecified. We show in extensive simulations
and real data examples that our new method, which we call AdaPT-GMM,
consistently delivers high power relative to competing state-of-the-art
methods. In particular, it performs well in scenarios where AdaPT is
underpowered, and is especially well-suited for testing composite null
hypothesis, such as whether the effect size exceeds a practical significance
threshold.
