# Metropolized Knockoff Sampling

arXiv: https://arxiv.org/abs/1903.00434 · HTML: https://mlsanity.com/paper/1903.00434/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2019.

## Built on by (most cited first, 10 of 10)

- [Conditional Feature Importance for Mixed Data](https://mlsanity.com/paper/2210.03047/) (2022)
- [Normalizing Flows for Knockoff-free Controlled Feature Selection](https://mlsanity.com/paper/2106.01528/) (2021)
- [GRASP: A Goodness-of-Fit Test for Classification Learning](https://mlsanity.com/paper/2209.02064/) (2022)
- [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)
- [The Conditional Prediction Function: A Novel Technique to Control False Discovery Rate for Complex Models](https://mlsanity.com/paper/2310.04919/) (2023)
- [CatNet: Controlling the False Discovery Rate in LSTM with SHAP Feature Importance and Gaussian Mirrors](https://mlsanity.com/paper/2411.16666/) (2024)
- [AICO: Feature Significance Tests for Supervised Learning](https://mlsanity.com/paper/2506.23396/) (2025)
- [Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features](https://mlsanity.com/paper/2604.07464/) (2026)
- [Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP](https://mlsanity.com/paper/2608.00989/) (2026)

## Abstract (arXiv)

Model-X knockoffs is a wrapper that transforms essentially any feature importance measure into a variable selection algorithm, which discovers true effects while rigorously controlling the expected fraction of false positives. A frequently discussed challenge to apply this method is to construct knockoff variables, which are synthetic variables obeying a crucial exchangeability property with the explanatory variables under study. This paper introduces techniques for knockoff generation in great generality: we provide a sequential characterization of all possible knockoff distributions, which leads to a Metropolis-Hastingsformulation of an exact knockoff sampler. We further show how to use conditional independence structure to speed up computations. Combining these two threads, we introduce an explicit set of sequential algorithms and empirically demonstrate their effectiveness. Our theoretical analysis proves that our algorithms achieve near-optimal computational complexity in certain cases. The techniques we develop are sufficiently rich to enable knockoff sampling in challenging models including cases where the covariates are continuous and heavy-tailed, and follow a graphical model such as the Ising model.