# Differentially Private False Discovery Rate Control

arXiv: https://arxiv.org/abs/1807.04209 · HTML: https://mlsanity.com/paper/1807.04209/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2018.

## Built on by (most cited first, 15 of 15)

- [Privacy Induces Robustness: Information-Computation Gaps and Sparse Mean Estimation](https://mlsanity.com/paper/2211.00724/) (2022)
- [Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning](https://mlsanity.com/paper/2303.07152/) (2023)
- [Oneshot Differentially Private Top-k Selection](https://mlsanity.com/paper/2105.08233/) (2021)
- [Adaptive Private-K-Selection with Adaptive K and Application to Multi-label PATE](https://mlsanity.com/paper/2203.16100/) (2022)
- [Efficient Sparse Least Absolute Deviation Regression with Differential Privacy](https://mlsanity.com/paper/2401.01294/) (2024)
- [High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guarantees](https://mlsanity.com/paper/2104.00245/) (2021)
- [Adaptive False Discovery Rate Control with Privacy Guarantee](https://mlsanity.com/paper/2305.19482/) (2023)
- [Differentially Private Federated Learning: Servers Trustworthiness, Estimation, and Statistical Inference](https://mlsanity.com/paper/2404.16287/) (2024)
- [Differentially Private Variable Selection via the Knockoff Filter](https://mlsanity.com/paper/2109.05402/) (2021)
- [Majority Vote for Distributed Differentially Private Sign Selection](https://mlsanity.com/paper/2209.04419/) (2022)
- [Differentially private sliced inverse regression in the federated paradigm](https://mlsanity.com/paper/2306.06324/) (2023)
- [FLIPHAT: Joint Differential Privacy for High Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2405.14038/) (2024)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Differentially Private Sliced Inverse Regression: Minimax Optimality and Algorithm](https://mlsanity.com/paper/2401.08150/) (2024)
- [Bayes-Nash Generative Privacy Against Membership Inference Attacks](https://mlsanity.com/paper/2410.07414/) (2024)

## Abstract (arXiv)

Differential privacy provides a rigorous framework for privacy-preserving data analysis. This paper proposes the first differentially private procedure for controlling the false discovery rate (FDR) in multiple hypothesis testing. Inspired by the Benjamini-Hochberg procedure (BHq), our approach is to first repeatedly add noise to the logarithms of the p-values to ensure differential privacy and to select an approximately smallest p-value serving as a promising candidate at each iteration; the selected p-values are further supplied to the BHq and our private procedure releases only the rejected ones. Moreover, we develop a new technique that is based on a backward submartingale for proving FDR control of a broad class of multiple testing procedures, including our private procedure, and both the BHq step-up and step-down procedures. As a novel aspect, the proof works for arbitrary dependence between the true null and false null test statistics, while FDR control is maintained up to a small multiplicative factor.