# Synthetic-Powered Multiple Testing with FDR Control

arXiv: https://arxiv.org/abs/2602.16690 · HTML: https://mlsanity.com/paper/2602.16690/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [OpenML-Python: an extensible Python API for OpenML](https://mlsanity.com/paper/1911.02490/) (2019)
- [Robust Conformal Outlier Detection under Contaminated Reference Data](https://mlsanity.com/paper/2502.04807/) (2025)
- [Synthetic-Powered Predictive Inference](https://mlsanity.com/paper/2505.13432/) (2025)
- [General Synthetic-Powered Inference](https://mlsanity.com/paper/2509.20345/) (2025)
- [Optimal Multiple Testing Under a Gaussian Prior on the Effect Sizes](https://mlsanity.com/paper/1504.02935/) (2015)
- [Weighted False Discovery Rate Control in Large-Scale Multiple Testing](https://mlsanity.com/paper/1508.01605/) (2015)
- [Elementary proofs of several results on false discovery rate](https://mlsanity.com/paper/2201.09350/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Regret Perspective on Online Multiple Testing](https://mlsanity.com/paper/2605.13916/) (2026)

## Abstract (arXiv)

Multiple hypothesis testing with false discovery rate (FDR) control is a fundamental problem in statistical inference, with broad applications in genomics, drug screening, and outlier detection. In many such settings, researchers may have access not only to real experimental observations but also to auxiliary or synthetic data -- from past, related experiments or generated by generative models -- that can provide additional evidence about the hypotheses of interest. We introduce SynthBH, a synthetic-powered multiple testing procedure that safely leverages such synthetic data. We prove that SynthBH guarantees finite-sample, distribution-free FDR control under a mild PRDS-type positive dependence condition, without requiring the pooled-data p-values to be valid under the null. The proposed method adapts to the (unknown) quality of the synthetic data: it enhances the sample efficiency and may boost the power when synthetic data are of high quality, while controlling the FDR at a user-specified level regardless of their quality. We demonstrate the empirical performance of SynthBH on tabular outlier detection benchmarks and on genomic analyses of drug-cancer sensitivity associations, and further study its properties through controlled experiments on simulated data.