# AdaPT-GMM: Powerful and robust covariate-assisted multiple testing

arXiv: https://arxiv.org/abs/2106.15812 · HTML: https://mlsanity.com/paper/2106.15812/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 55 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 18 of 18)

- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [ADDIS: an adaptive discarding algorithm for online FDR control with conservative nulls](https://mlsanity.com/paper/1905.11465/) (2019)
- [Conditional calibration for false discovery rate control under dependence](https://mlsanity.com/paper/2007.10438/) (2020)
- [False discovery rate regression: an application to neural synchrony detection in primary visual cortex](https://mlsanity.com/paper/1307.3495/) (2013)
- [Covariate powered cross-weighted multiple testing](https://mlsanity.com/paper/1701.05179/) (2017)
- [Black Box FDR](https://mlsanity.com/paper/1806.03143/) (2018)
- [Optimal Multiple Testing Under a Gaussian Prior on the Effect Sizes](https://mlsanity.com/paper/1504.02935/) (2015)
- [Sequential Selection Procedures and False Discovery Rate Control](https://mlsanity.com/paper/1309.5352/) (2013)
- [Accumulation tests for FDR control in ordered hypothesis testing](https://mlsanity.com/paper/1505.07352/) (2015)
- [On Procedures Controlling the FDR for Testing Hierarchically Ordered Hypotheses](https://mlsanity.com/paper/1612.04467/) (2016)
- [Optimal False Discovery Rate Control for Large Scale Multiple Testing with Auxiliary Information](https://mlsanity.com/paper/2103.15311/) (2021)
- [Power of Ordered Hypothesis Testing](https://mlsanity.com/paper/1606.01969/) (2016)
- [Knockoffs with Side Information](https://mlsanity.com/paper/2001.07835/) (2020)
- [Multiple testing when many p-values are uniformly conservative, with application to testing qualitative interaction in educational interventions](https://mlsanity.com/paper/1703.09787/) (2017)
- [Gaining power in multiple testing of interval hypotheses via conditionalization](https://mlsanity.com/paper/1801.00141/) (2017)
- [Familywise Error Rate Control by Interactive Unmasking](https://mlsanity.com/paper/2002.08545/) (2020)

## Abstract (arXiv)

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.