# Improving the Stability of the Knockoff Procedure: Multiple Simultaneous Knockoffs and Entropy Maximization

arXiv: https://arxiv.org/abs/1810.11378 · HTML: https://mlsanity.com/paper/1810.11378/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2018.

## Built on by (most cited first, 7 of 7)

- [Deep neural networks with controlled variable selection for the identification of putative causal genetic variants](https://mlsanity.com/paper/2109.14719/) (2021)
- [Ensembling improves stability and power of feature selection for deep learning models](https://mlsanity.com/paper/2210.00604/) (2022)
- [Near-optimal multiple testing in Bayesian linear models with finite-sample FDR control](https://mlsanity.com/paper/2211.02778/) (2022)
- [Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs](https://mlsanity.com/paper/2605.26631/) (2026)
- [Knoop: Practical Enhancement of Knockoff with Over-Parameterization for Variable Selection](https://mlsanity.com/paper/2501.17889/) (2025)
- [Interpretable Feature Interaction via Statistical Self-supervised Learning on Tabular Data](https://mlsanity.com/paper/2503.18048/) (2025)
- [GRIP2: A Robust and Powerful Deep Knockoff Method for Feature Selection](https://mlsanity.com/paper/2602.00218/) (2026)

## Abstract (arXiv)

The Model-X knockoff procedure has recently emerged as a powerful approach for feature selection with statistical guarantees. The advantage of knockoff is that if we have a good model of the features X, then we can identify salient features without knowing anything about how the outcome Y depends on X. An important drawback of knockoffs is its instability: running the procedure twice can result in very different selected features, potentially leading to different conclusions. Addressing this instability is critical for obtaining reproducible and robust results. Here we present a generalization of the knockoff procedure that we call simultaneous multi-knockoffs. We show that multi-knockoff guarantees false discovery rate (FDR) control, and is substantially more stable and powerful compared to the standard (single) knockoff. Moreover we propose a new algorithm based on entropy maximization for generating Gaussian multi-knockoffs. We validate the improved stability and power of multi-knockoffs in systematic experiments. We also illustrate how multi-knockoffs can improve the accuracy of detecting genetic mutations that are causally linked to phenotypes.