# Controlling the FDR in variable selection via multiple knockoffs

arXiv: https://arxiv.org/abs/1911.09442 · HTML: https://mlsanity.com/paper/1911.09442/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

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

- [Knockoff-Guided Compressive Sensing: A Statistical Machine Learning Framework for Support-Assured Signal Recovery](https://mlsanity.com/paper/2505.24727/) (2025)

## Abstract (arXiv)

Barber and Candes recently introduced a feature selection method called knockoff+ that controls the false discovery rate (FDR) among the selected features in the classical linear regression problem. Knockoff+ uses the competition between the original features and artificially created knockoff features to control the FDR [1]. We generalize Barber and Candes' knockoff construction to generate multiple knockoffs and use those in conjunction with a recently developed general framework for multiple competition-based FDR control [9]. We prove that using our initial multiple-knockoff construction the combined procedure rigorously controls the FDR in the finite sample setting. Because this construction has a somewhat limited utility we introduce a heuristic we call "batching" which significantly improves the power of our multiple-knockoff procedures. Finally, we combine the batched knockoffs with a new context-dependent resampling scheme that replaces the generic resampling scheme used in the general multiple-competition setup. We show using simulations that the resulting "multi-knockoff-select" procedure empirically controls the FDR in the finite setting of the variable selection problem while often delivering substantially more power than knockoff+.