# Deep Knockoffs

arXiv: https://arxiv.org/abs/1811.06687 · HTML: https://mlsanity.com/paper/1811.06687/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2018.

## Built on by (most cited first, 30 of 41)

- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [The good, the bad and the ugly sides of data augmentation: An implicit spectral regularization perspective](https://mlsanity.com/paper/2210.05021/) (2022)
- [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)
- [Conditional Feature Importance for Mixed Data](https://mlsanity.com/paper/2210.03047/) (2022)
- [Sequential Knockoffs for Variable Selection in Reinforcement Learning](https://mlsanity.com/paper/2303.14281/) (2023)
- [Normalizing Flows for Knockoff-free Controlled Feature Selection](https://mlsanity.com/paper/2106.01528/) (2021)
- [Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders](https://mlsanity.com/paper/2201.00073/) (2021)
- [Time Series Causal Link Estimation under Hidden Confounding using Knockoff Interventions](https://mlsanity.com/paper/2209.11497/) (2022)
- [Counterfactual Generation with Knockoffs](https://mlsanity.com/paper/2102.00951/) (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)
- [Statistically Significant Concept-based Explanation of Image Classifiers via Model Knockoffs](https://mlsanity.com/paper/2305.18362/) (2023)
- [Causal Inference in Non-linear Time-series using Deep Networks and Knockoff Counterfactuals](https://mlsanity.com/paper/2109.10817/) (2021)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [DIET: Conditional independence testing with marginal dependence measures of residual information](https://mlsanity.com/paper/2208.08579/) (2022)
- [Efficient Multimodal Sampling via Tempered Distribution Flow](https://mlsanity.com/paper/2304.03933/) (2023)
- [High-Dimensional False Discovery Rate Control for Dependent Variables](https://mlsanity.com/paper/2401.15796/) (2024)
- [Learning to Increase the Power of Conditional Randomization Tests](https://mlsanity.com/paper/2207.01022/) (2022)
- [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)
- [DeepROCK: Error-controlled interaction detection in deep neural networks](https://mlsanity.com/paper/2309.15319/) (2023)
- [DeepFDR: A Deep Learning-based False Discovery Rate Control Method for Neuroimaging Data](https://mlsanity.com/paper/2310.13349/) (2023)
- [DeepDRK: Deep Dependency Regularized Knockoff for Feature Selection](https://mlsanity.com/paper/2402.17176/) (2024)
- [Knoop: Practical Enhancement of Knockoff with Over-Parameterization for Variable Selection](https://mlsanity.com/paper/2501.17889/) (2025)
- [Provable FDR Control for Deep Feature Selection: Deep MLPs and Beyond](https://mlsanity.com/paper/2512.04696/) (2025)
- [High-dimensional Inference and FDR Control for Simulated Markov Random Fields](https://mlsanity.com/paper/2202.05612/) (2022)
- [Variable Selection with the Knockoffs: Composite Null Hypotheses](https://mlsanity.com/paper/2203.02849/) (2022)
- [Error Controlled Feature Selection for Ultrahigh Dimensional and Highly Correlated Feature Space Using Deep Learning](https://mlsanity.com/paper/2209.07011/) (2022)
- [The Conditional Prediction Function: A Novel Technique to Control False Discovery Rate for Complex Models](https://mlsanity.com/paper/2310.04919/) (2023)

## Abstract (arXiv)

This paper introduces a machine for sampling approximate model-X knockoffs for arbitrary and unspecified data distributions using deep generative models. The main idea is to iteratively refine a knockoff sampling mechanism until a criterion measuring the validity of the produced knockoffs is optimized; this criterion is inspired by the popular maximum mean discrepancy in machine learning and can be thought of as measuring the distance to pairwise exchangeability between original and knockoff features. By building upon the existing model-X framework, we thus obtain a flexible and model-free statistical tool to perform controlled variable selection. Extensive numerical experiments and quantitative tests confirm the generality, effectiveness, and power of our deep knockoff machines. Finally, we apply this new method to a real study of mutations linked to changes in drug resistance in the human immunodeficiency virus.