# Controlling the false discovery rate via knockoffs

arXiv: https://arxiv.org/abs/1404.5609 · HTML: https://mlsanity.com/paper/1404.5609/

## Key facts

- Cited by 97 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2014.

## Built on by (most cited first, 30 of 97)

- [Feature Importance: A Closer Look at Shapley Values and LOCO](https://mlsanity.com/paper/2303.05981/) (2023)
- [Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery](https://mlsanity.com/paper/2301.12649/) (2023)
- [Derandomized Novelty Detection with FDR Control via Conformal E-values](https://mlsanity.com/paper/2302.07294/) (2023)
- [Knockoff-Guided Feature Selection via A Single Pre-trained Reinforced Agent](https://mlsanity.com/paper/2403.04015/) (2024)
- [Data fission: splitting a single data point](https://mlsanity.com/paper/2112.11079/) (2021)
- [Model-X Sequential Testing for Conditional Independence via Testing by Betting](https://mlsanity.com/paper/2210.00354/) (2022)
- [Composite Feature Selection using Deep Ensembles](https://mlsanity.com/paper/2211.00631/) (2022)
- [The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control](https://mlsanity.com/paper/2110.06048/) (2021)
- [Task-Agnostic Machine-Learning-Assisted Inference](https://mlsanity.com/paper/2405.20039/) (2024)
- [Conformal link prediction for false discovery rate control](https://mlsanity.com/paper/2306.14693/) (2023)
- [Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning](https://mlsanity.com/paper/2102.12328/) (2021)
- [Sequential Knockoffs for Variable Selection in Reinforcement Learning](https://mlsanity.com/paper/2303.14281/) (2023)
- [Adaptive debiased machine learning using data-driven model selection techniques](https://mlsanity.com/paper/2307.12544/) (2023)
- [Time Series Causal Link Estimation under Hidden Confounding using Knockoff Interventions](https://mlsanity.com/paper/2209.11497/) (2022)
- [FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking](https://mlsanity.com/paper/2401.15139/) (2024)
- [Counterfactual Generation with Knockoffs](https://mlsanity.com/paper/2102.00951/) (2021)
- [Deep neural networks with controlled variable selection for the identification of putative causal genetic variants](https://mlsanity.com/paper/2109.14719/) (2021)
- [Multivariate rank via entropic optimal transport: sample efficiency and generative modeling](https://mlsanity.com/paper/2111.00043/) (2021)
- [Causal Discovery using Model Invariance through Knockoff Interventions](https://mlsanity.com/paper/2207.04055/) (2022)
- [Sparse PCA with False Discovery Rate Controlled Variable Selection](https://mlsanity.com/paper/2401.08375/) (2024)
- [Causal Inference in Non-linear Time-series using Deep Networks and Knockoff Counterfactuals](https://mlsanity.com/paper/2109.10817/) (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)
- [High-Dimensional False Discovery Rate Control for Dependent Variables](https://mlsanity.com/paper/2401.15796/) (2024)
- [Indirectly Parameterized Concrete Autoencoders](https://mlsanity.com/paper/2403.00563/) (2024)
- [Deep Nonparametric Conditional Independence Tests for Images](https://mlsanity.com/paper/2411.06140/) (2024)
- [Directional FDR Control for Sub-Gaussian Sparse GLMs](https://mlsanity.com/paper/2105.00393/) (2021)
- [PPFS: Predictive Permutation Feature Selection](https://mlsanity.com/paper/2110.10713/) (2021)
- [Distributed Sparse Feature Selection in Communication-Restricted Networks](https://mlsanity.com/paper/2111.02802/) (2021)
- [A Conditional Randomization Test for Sparse Logistic Regression in High-Dimension](https://mlsanity.com/paper/2205.14613/) (2022)

## Abstract (arXiv)

In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR) - the expected fraction of false discoveries among all discoveries - is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, or the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. As the name suggests, the method operates by manufacturing knockoff variables that are cheap - their construction does not require any new data - and are designed to mimic the correlation structure found within the existing variables, in a way that allows for accurate FDR control, beyond what is possible with permutation-based methods. The method of knockoffs is very general and flexible, and can work with a broad class of test statistics. We test the method in combination with statistics from the Lasso for sparse regression, and obtain empirical results showing that the resulting method has far more power than existing selection rules when the proportion of null variables is high.