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

• URL: http://arxiv.org/abs/2409.19088v1
• Date: Fri, 27 Sep 2024 18:38:51 GMT
• Title: Solving FDR-Controlled Sparse Regression Problems with Five Million Variables on a Laptop
• Authors: Fabian Scheidt, Jasin Machkour, Michael Muma,
• Abstract summary: T-Rex selector is a new learning framework based on early terminated random experiments with computer-generated dummy variables. We propose the Big T-Rex, a new implementation of T-Rex that drastically reduces its Random Access Memory (RAM) consumption. 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.
• Score: 1.5948860527881505
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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