The Terminating-Knockoff Filter: Fast High-Dimensional Variable Selection with False Discovery Rate Control

We propose the Terminating-Knockoff (T-Knock) filter, a fast variable selection method for high-dimensional data. The T-Knock filter 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 knockoff predictors. A finite sample proof based on martingale theory for the FDR control property is provided. Numerical simulations show that the FDR is controlled at the target level while allowing for a high power. We prove under mild conditions that the knockoffs can be sampled from any univariate probability distribution with existing finite expectation and variance. The computational complexity of the proposed method is derived and it is demonstrated via numerical simulations that the sequential computation time is multiple orders of magnitude lower than that of the strongest benchmark methods in sparse high-dimensional settings. The T-Knock filter outperforms state-of-the-art methods for FDR control on a simulated genome-wide association study (GWAS), while its computation time is more than two orders of magnitude lower than that of the strongest benchmark methods. An open source R package containing the implementation of the T-Knock filter is available at https://github.com/jasinmachkour/tknock.