# Simultaneous false discovery proportion bounds via knockoffs and closed testing

arXiv: https://arxiv.org/abs/2212.12822 · HTML: https://mlsanity.com/paper/2212.12822/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2022.

## Built on by (most cited first, 3 of 3)

- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [Class conditional conformal prediction for multiple inputs by p-value aggregation](https://mlsanity.com/paper/2507.07150/) (2025)
- [Everywhere Valid Bounds on False Discovery Proportions in Conformal Inference](https://mlsanity.com/paper/2605.20726/) (2026)

## Abstract (arXiv)

We propose new methods to obtain simultaneous false discovery proportion bounds for knockoff-based approaches. We first investigate an approach based on Janson and Su's k-familywise error rate control method and interpolation. We then generalize it by considering a collection of k values, and show that the bound of Katsevich and Ramdas is a special case of this method and can be uniformly improved. Next, we further generalize the method by using closed testing with a multi-weighted-sum local test statistic. This allows us to obtain a further uniform improvement and other generalizations over previous methods. We also develop an efficient shortcut for its implementation. We compare the performance of our proposed methods in simulations and apply them to a data set from the UK Biobank.