# Conditional calibration for false discovery rate control under dependence

arXiv: https://arxiv.org/abs/2007.10438 · HTML: https://mlsanity.com/paper/2007.10438/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jul 2020.

## Built on by (most cited first, 11 of 11)

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- [Integrative conformal p-values for powerful out-of-distribution testing with labeled outliers](https://mlsanity.com/paper/2208.11111/) (2022)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Near-optimal multiple testing in Bayesian linear models with finite-sample FDR control](https://mlsanity.com/paper/2211.02778/) (2022)
- [Membership Inference Attacks with False Discovery Rate Control](https://mlsanity.com/paper/2508.07066/) (2025)
- [Online False Discovery Rate Control for LORD & SAFFRON Under Positive, Local Dependence](https://mlsanity.com/paper/2110.08161/) (2021)
- [AdaPT-GMM: Powerful and robust covariate-assisted multiple testing](https://mlsanity.com/paper/2106.15812/) (2021)
- [Variable Selection with the Knockoffs: Composite Null Hypotheses](https://mlsanity.com/paper/2203.02849/) (2022)
- [Falsifying Discriminant Validity of Predictive Algorithms](https://mlsanity.com/paper/2601.17146/) (2026)
- [Safe Urban Traffic Control via Uncertainty-Aware Conformal Prediction and World-Model Reinforcement Learning](https://mlsanity.com/paper/2602.04821/) (2026)
- [The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests](https://mlsanity.com/paper/2607.12208/) (2026)

## Abstract (arXiv)

We introduce a new class of methods for finite-sample false discovery rate (FDR) control in multiple testing problems with dependent test statistics where the dependence is fully or partially known. Our approach separately calibrates a data-dependent p-value rejection threshold for each hypothesis, relaxing or tightening the threshold as appropriate to target exact FDR control. In addition to our general framework we propose a concrete algorithm, the dependence-adjusted Benjamini-Hochberg (dBH) procedure, which adaptively thresholds the q-value for each hypothesis. Under positive regression dependence the dBH procedure uniformly dominates the standard BH procedure, and in general it uniformly dominates the Benjamini-Yekutieli (BY) procedure (also known as BH with log correction). Simulations and real data examples illustrate power gains over competing approaches to FDR control under dependence.