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

TL;DR

The paper introduces T-Rex, a fast and scalable variable selection method for high-dimensional data that controls false discovery rate effectively, outperforming existing methods in accuracy and computational efficiency.

Contribution

The T-Rex selector fuses multiple early terminated random experiments to control FDR while maximizing variable selection, with proven theoretical guarantees and practical efficiency.

Findings

Controls FDR at target level with high power

Outperforms state-of-the-art methods in simulations

Computational time is over 100 times faster than benchmarks

Abstract

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.