# ARK: Robust Knockoffs Inference with Coupling

arXiv: https://arxiv.org/abs/2307.04400 · HTML: https://mlsanity.com/paper/2307.04400/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 44 references that are in the map.
- First posted on arXiv 10 Jul 2023.

## Builds on (most cited first, 3 of 3)

- [Derandomized knockoffs: leveraging e-values for false discovery rate control](https://mlsanity.com/paper/2205.15461/) (2022)
- [High-Dimensional Knockoffs Inference for Time Series Data](https://mlsanity.com/paper/2112.09851/) (2021)
- [Controlling the False Discovery Rate in Transformational Sparsity: Split Knockoffs](https://mlsanity.com/paper/2103.16159/) (2021)

## Abstract (arXiv)

We investigate the robustness of the model-X knockoffs framework with respect to the misspecified or estimated feature distribution. We achieve such a goal by theoretically studying the feature selection performance of a practically implemented knockoffs algorithm, which we name as the approximate knockoffs (ARK) procedure, under the measures of the false discovery rate (FDR) and k-familywise error rate (k-FWER). The approximate knockoffs procedure differs from the model-X knockoffs procedure only in that the former uses the misspecified or estimated feature distribution. A key technique in our theoretical analyses is to couple the approximate knockoffs procedure with the model-X knockoffs procedure so that random variables in these two procedures can be close in realizations. We prove that if such coupled model-X knockoffs procedure exists, the approximate knockoffs procedure can achieve the asymptotic FDR or k-FWER control at the target level. We showcase three specific constructions of such coupled model-X knockoff variables, verifying their existence and justifying the robustness of the model-X knockoffs framework. Additionally, we formally connect our concept of knockoff variable coupling to a type of Wasserstein distance.