  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.
