# The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control

arXiv: https://arxiv.org/abs/2110.06048 · HTML: https://mlsanity.com/paper/2110.06048/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 73 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 10 of 10)

- [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)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [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)
- [A significance test for the lasso](https://mlsanity.com/paper/1301.7161/) (2013)
- [Gene Hunting with Knockoffs for Hidden Markov Models](https://mlsanity.com/paper/1706.04677/) (2017)
- [Derandomizing Knockoffs](https://mlsanity.com/paper/2012.02717/) (2020)

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

- [FDR-Controlled Portfolio Optimization for Sparse Financial Index Tracking](https://mlsanity.com/paper/2401.15139/) (2024)
- [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)
- [The Informed Elastic Net for Fast Grouped Variable Selection and FDR Control in Genomics Research](https://mlsanity.com/paper/2410.05211/) (2024)
- [Knockoff-Guided Compressive Sensing: A Statistical Machine Learning Framework for Support-Assured Signal Recovery](https://mlsanity.com/paper/2505.24727/) (2025)
- [Reproducible Physiological Features in Affective Computing: A Preliminary Analysis on Arousal Modeling](https://mlsanity.com/paper/2508.10561/) (2025)
- [Learning False Discovery Rate Control via Model-Based Neural Networks](https://mlsanity.com/paper/2602.05798/) (2026)
- [Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Features](https://mlsanity.com/paper/2604.07464/) (2026)

## Abstract (arXiv)

We propose the Terminating-Random Experiments (T-Rex) selector, a fast variable selection method for high-dimensional data. The T-Rex selector controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. This is achieved by fusing the solutions of multiple early terminated random experiments. The experiments are conducted on a combination of the original predictors and multiple sets of randomly generated dummy predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations confirm that the FDR is controlled at the target level while allowing for high power. We prove that the dummies can be sampled from any univariate probability distribution with finite expectation and variance. The computational complexity of the proposed method is linear in the number of variables. The T-Rex selector outperforms state-of-the-art methods for FDR control in numerical experiments and on a simulated genome-wide association study (GWAS), while its sequential computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. The open source R package TRexSelector containing the implementation of the T-Rex selector is available on CRAN.