# Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features

arXiv: https://arxiv.org/abs/2604.07464 · HTML: https://mlsanity.com/paper/2604.07464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Controlling the false discovery rate via knockoffs](https://mlsanity.com/paper/1404.5609/) (2014)
- [Deep Knockoffs](https://mlsanity.com/paper/1811.06687/) (2018)
- [False Discoveries Occur Early on the Lasso Path](https://mlsanity.com/paper/1511.01957/) (2015)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [Derandomized knockoffs: leveraging e-values for false discovery rate control](https://mlsanity.com/paper/2205.15461/) (2022)
- [A General Framework for Fast Stagewise Algorithms](https://mlsanity.com/paper/1408.5801/) (2014)
- [The knockoff filter for FDR control in group-sparse and multitask regression](https://mlsanity.com/paper/1602.03589/) (2016)
- [Metropolized Knockoff Sampling](https://mlsanity.com/paper/1903.00434/) (2019)
- [Controlling False Discovery Rate Using Gaussian Mirrors](https://mlsanity.com/paper/1911.09761/) (2019)
- [The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control](https://mlsanity.com/paper/2110.06048/) (2021)
- [Derandomizing Knockoffs](https://mlsanity.com/paper/2012.02717/) (2020)
- [Powerful Knockoffs via Minimizing Reconstructability](https://mlsanity.com/paper/2011.14625/) (2020)
- [FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking](https://mlsanity.com/paper/2401.15139/) (2024)
- [Outlier Robust and Sparse Estimation of Linear Regression Coefficients](https://mlsanity.com/paper/2208.11592/) (2022)
- [Sparse PCA with False Discovery Rate Controlled Variable Selection](https://mlsanity.com/paper/2401.08375/) (2024)
- [False Discovery Rate Control for Gaussian Graphical Models via Neighborhood Screening](https://mlsanity.com/paper/2401.09979/) (2024)
- [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)
- [FANOK: Knockoffs in Linear Time](https://mlsanity.com/paper/2006.08790/) (2020)
- [The Informed Elastic Net for Fast Grouped Variable Selection and FDR Control in Genomics Research](https://mlsanity.com/paper/2410.05211/) (2024)

## Abstract (arXiv)

High-dimensional variable selection, particularly in genomics, requires error-controlling procedures that scale to millions of predictors. The Terminating-Random Experiments (T-Rex) selector achieves false discovery rate (FDR) control by aggregating results of early terminated random experiments, each combining original predictors with i.i.d. synthetic null variables (dummies). At biobank scales, however, explicit dummy augmentation requires terabytes of memory. We demonstrate that this bottleneck is not fundamental. Formalizing the information flow of forward selection through a filtration, we show that compatible selectors interact with unselected dummies solely through projections onto an adaptively evolving low-dimensional subspace. For rotationally invariant dummy distributions, we derive an adaptive stick-breaking construction sampling these projections from their exact conditional distribution given the selection history, thereby eliminating dummy matrix materialization. We prove a pathwise universality theorem: under mild delocalization conditions, selection paths driven by generic standardized i.i.d. dummies converge to the same Gaussian limit. We instantiate the theory through Virtual Dummy LARS (VD-LARS), reducing memory and runtime by several orders of magnitude while preserving the exact selection law and FDR guarantees of the T-Rex selector. Experiments on realistic genome-wide association study data confirm that VD-T-Rex controls FDR and achieves power at scales where all competing methods either fail or time out.