# A knockoff filter for high-dimensional selective inference

arXiv: https://arxiv.org/abs/1602.03574 · HTML: https://mlsanity.com/paper/1602.03574/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2016.

## Built on by (most cited first, 25 of 25)

- [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)
- [Interpretable Machine Learning for Discovery: Statistical Challenges & Opportunities](https://mlsanity.com/paper/2308.01475/) (2023)
- [Lazy Estimation of Variable Importance for Large Neural Networks](https://mlsanity.com/paper/2207.09097/) (2022)
- [BEAUTY Powered BEAST](https://mlsanity.com/paper/2103.00674/) (2021)
- [High-Dimensional False Discovery Rate Control for Dependent Variables](https://mlsanity.com/paper/2401.15796/) (2024)
- [Solving FDR-Controlled Sparse Regression Problems with Five Million Variables on a Laptop](https://mlsanity.com/paper/2409.19088/) (2024)
- [Data-driven sparse identification of governing PDEs via knockoff filters and multi-criteria trade-offs](https://mlsanity.com/paper/2605.26631/) (2026)
- [Differentially Private Variable Selection via the Knockoff Filter](https://mlsanity.com/paper/2109.05402/) (2021)
- [Error-based Knockoffs Inference for Controlled Feature Selection](https://mlsanity.com/paper/2203.04483/) (2022)
- [Black-box Selective Inference via Bootstrapping](https://mlsanity.com/paper/2203.14504/) (2022)
- [Knockoffs-SPR: Clean Sample Selection in Learning with Noisy Labels](https://mlsanity.com/paper/2301.00545/) (2023)
- [Deep Learning-based Group Causal Inference in Multivariate Time-series](https://mlsanity.com/paper/2401.08386/) (2024)
- [Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection](https://mlsanity.com/paper/2405.03063/) (2024)
- [Functional relevance based on the continuous Shapley value](https://mlsanity.com/paper/2411.18575/) (2024)
- [Knoop: Practical Enhancement of Knockoff with Over-Parameterization for Variable Selection](https://mlsanity.com/paper/2501.17889/) (2025)
- [Variable Selection with the Knockoffs: Composite Null Hypotheses](https://mlsanity.com/paper/2203.02849/) (2022)
- [CatNet: Controlling the False Discovery Rate in LSTM with SHAP Feature Importance and Gaussian Mirrors](https://mlsanity.com/paper/2411.16666/) (2024)
- [Knockoff-Guided Compressive Sensing: A Statistical Machine Learning Framework for Support-Assured Signal Recovery](https://mlsanity.com/paper/2505.24727/) (2025)
- [Experimental Analysis of Productive Interaction Strategy with ChatGPT: User Study on Function and Project-level Code Generation Tasks](https://mlsanity.com/paper/2508.04125/) (2025)
- [Sparse minimum Redundancy Maximum Relevance for feature selection](https://mlsanity.com/paper/2508.18901/) (2025)
- [Group Interventions on Deep Networks for Causal Discovery in Subsystems](https://mlsanity.com/paper/2510.23906/) (2025)
- [Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features](https://mlsanity.com/paper/2604.07464/) (2026)
- [Knockoffs-based False Discovery Rate Control and Simplification for Deep Neural Networks](https://mlsanity.com/paper/2606.04404/) (2026)
- [Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP](https://mlsanity.com/paper/2608.00989/) (2026)

## Abstract (arXiv)

This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units. In this framework, the observations are split into two groups, where the first group is used to screen for a set of potentially relevant variables, whereas the second is used for inference over this reduced set of variables; we also develop strategies for leveraging information from the first part of the data at the inference step for greater power. In our work, the inferential step is carried out by applying the recently introduced knockoff filter, which creates a knockoff copy-a fake variable serving as a control-for each screened variable. We prove that this procedure controls the directional false discovery rate (FDR) in the reduced model controlling for all screened variables; this says that our high-dimensional knockoff procedure 'discovers' important variables as well as the directions (signs) of their effects, in such a way that the expected proportion of wrongly chosen signs is below the user-specified level (thereby controlling a notion of Type S error averaged over the selected set). This result is non-asymptotic, and holds for any distribution of the original features and any values of the unknown regression coefficients, so that inference is not calibrated under hypothesized values of the effect sizes. We demonstrate the performance of our general and flexible approach through numerical studies, showing more power than existing alternatives. Finally, we apply our method to a genome-wide association study to find locations on the genome that are possibly associated with a continuous phenotype.