# Solving FDR-Controlled Sparse Regression Problems with Five Million Variables on a Laptop

arXiv: https://arxiv.org/abs/2409.19088 · HTML: https://mlsanity.com/paper/2409.19088/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 27 Sep 2024.

## Builds on (most cited first, 4 of 4)

- [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)
- [A knockoff filter for high-dimensional selective inference](https://mlsanity.com/paper/1602.03574/) (2016)
- [The Terminating-Random Experiments Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control](https://mlsanity.com/paper/2110.06048/) (2021)

## Built on by (most cited first, 2 of 2)

- [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)

Currently, there is an urgent demand for scalable multivariate and high-dimensional false discovery rate (FDR)-controlling variable selection methods to ensure the repro-ducibility of discoveries. However, among existing methods, only the recently proposed Terminating-Random Experiments (T-Rex) selector scales to problems with millions of variables, as encountered in, e.g., genomics research. The T-Rex selector is a new learning framework based on early terminated random experiments with computer-generated dummy variables. In this work, we propose the Big T-Rex, a new implementation of T-Rex that drastically reduces its Random Access Memory (RAM) consumption to enable solving FDR-controlled sparse regression problems with millions of variables on a laptop. We incorporate advanced memory-mapping techniques to work with matrices that reside on solid-state drive and two new dummy generation strategies based on permutations of a reference matrix. Our nu-merical experiments demonstrate a drastic reduction in memory demand and computation time. We showcase that the Big T-Rex can efficiently solve FDR-controlled Lasso-type problems with five million variables on a laptop in thirty minutes. Our work empowers researchers without access to high-performance clusters to make reproducible discoveries in large-scale high-dimensional data.