# Finite Resources False Discovery Rate Control in Structured Hypothesis Spaces

arXiv: https://arxiv.org/abs/2606.15393 · HTML: https://mlsanity.com/paper/2606.15393/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Constructing Domain-Specific Evaluation Sets for LLM-as-a-judge](https://mlsanity.com/paper/2408.08808/) (2024)
- [AdaPT: An interactive procedure for multiple testing with side information](https://mlsanity.com/paper/1609.06035/) (2016)
- [Robust inference with knockoffs](https://mlsanity.com/paper/1801.03896/) (2018)
- [False discovery rate smoothing](https://mlsanity.com/paper/1411.6144/) (2014)
- [Adaptive Monte Carlo Multiple Testing via Multi-Armed Bandits](https://mlsanity.com/paper/1902.00197/) (2019)
- [STRAW: Structure-Adaptive Weighting Procedure for Large-Scale Spatial Multiple Testing](https://mlsanity.com/paper/2309.15699/) (2023)
- [Online Resource Allocation with Average Budget Constraints](https://mlsanity.com/paper/2402.11425/) (2024)
- [Controlling False Discovery in Arbitrarily Structured Hypothesis Spaces via Reproducing Kernels](https://mlsanity.com/paper/2605.17559/) (2026)

## Abstract (arXiv)

Scientific discovery relies on large-scale hypothesis testing. However, the capacity to identify true discoveries while controlling false discovery faces major challenges: obtaining relevant reference data (the null distribution) is resource-intensive, leaving finite-data uncertainty, and the procedure should account for the inherent structure in the hypothesis space, when such structure exists. Here, we present a framework for controlling the false discovery rate both when each hypothesis is evidenced only by a finite count of null draws, leaving its p-value uncertain, and when the hypothesis space carries arbitrary structure, requiring only that the structure be represented through a suitable reproducing kernel. We present two decision rules that are both robust to structural mis-specification, yet offer a distinct trade-off between exact FDR control and statistical power. The first rule guarantees exact FDR control; the second maximizes power by adapting mirror-statistic control into count space, utilizing an analytical framework to assess FDR control when exact mirror symmetry is relaxed. Furthermore, the tractability gained by the RKHS framework allows us to directly investigate finite-data uncertainties, which we leverage to suggest a policy for the efficient allocation of null distribution samples.