# Normalizing Flows for Knockoff-free Controlled Feature Selection

arXiv: https://arxiv.org/abs/2106.01528 · HTML: https://mlsanity.com/paper/2106.01528/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 47 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 13 of 13)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [Gaussianization Flows](https://mlsanity.com/paper/2003.01941/) (2020)
- [Fast and Powerful Conditional Randomization Testing via Distillation](https://mlsanity.com/paper/2006.03980/) (2020)
- [Deep Direct Likelihood Knockoffs](https://mlsanity.com/paper/2007.15835/) (2020)
- [The knockoff filter for FDR control in group-sparse and multitask regression](https://mlsanity.com/paper/1602.03589/) (2016)
- [Knockoffs for the mass: new feature importance statistics with false discovery guarantees](https://mlsanity.com/paper/1807.06214/) (2018)
- [Metropolized Knockoff Sampling](https://mlsanity.com/paper/1903.00434/) (2019)
- [Auto-Encoding Knockoff Generator for FDR Controlled Variable Selection](https://mlsanity.com/paper/1809.10765/) (2018)
- [RANK: Large-Scale Inference with Graphical Nonlinear Knockoffs](https://mlsanity.com/paper/1709.00092/) (2017)

## Built on by (most cited first, 5 of 5)

- [Training Normalizing Flows from Dependent Data](https://mlsanity.com/paper/2209.14933/) (2022)
- [DeepDRK: Deep Dependency Regularized Knockoff for Feature Selection](https://mlsanity.com/paper/2402.17176/) (2024)
- [Experimental Design for Multi-Channel Imaging via Task-Driven Feature Selection](https://mlsanity.com/paper/2210.06891/) (2022)
- [Kernelised Normalising Flows](https://mlsanity.com/paper/2307.14839/) (2023)
- [Model-Agnostic FDR Control via Group Gaussian Mirror and Permutation SHAP](https://mlsanity.com/paper/2608.00989/) (2026)

## Abstract (arXiv)

Controlled feature selection aims to discover the features a response depends on while limiting the false discovery rate (FDR) to a predefined level. Recently, multiple deep-learning-based methods have been proposed to perform controlled feature selection through the Model-X knockoff framework. We demonstrate, however, that these methods often fail to control the FDR for two reasons. First, these methods often learn inaccurate models of features. Second, the "swap" property, which is required for knockoffs to be valid, is often not well enforced. We propose a new procedure called FlowSelect to perform controlled feature selection that does not suffer from either of these two problems. To more accurately model the features, FlowSelect uses normalizing flows, the state-of-the-art method for density estimation. Instead of enforcing the "swap" property, FlowSelect uses a novel MCMC-based procedure to calculate p-values for each feature directly. Asymptotically, FlowSelect computes valid p-values. Empirically, FlowSelect consistently controls the FDR on both synthetic and semi-synthetic benchmarks, whereas competing knockoff-based approaches do not. FlowSelect also demonstrates greater power on these benchmarks. Additionally, FlowSelect correctly infers the genetic variants associated with specific soybean traits from GWAS data.