SyNPar: Synthetic Null Data Parallelism for High-Power False Discovery Rate Control in High-Dimensional Variable Selection

Abstract: Balancing false discovery rate (FDR) and statistical power to ensure reliable discoveries is a key challenge in high-dimensional variable selection. Although several FDR control methods have been proposed, most involve perturbing the original data, either by concatenating knockoff variables or splitting the data into two halves, both of which can lead to a loss of power. In this paper, we introduce a novel approach called Synthetic Null Parallelism (SyNPar), which controls the FDR in high-dimensional variable selection while preserving the original data. SyNPar generates synthetic null data from a model fitted to the original data and modified to reflect the null hypothesis. It then applies the same estimation procedure in parallel to both the original and synthetic null data to estimate coefficients that indicate feature importance. By comparing the coefficients estimated from the null data with those from the original data, SyNPar effectively identifies false positives, functioning as a numerical analog of a likelihood ratio test. We provide theoretical guarantees for FDR control at any desired level while ensuring that the power approaches one with high probability asymptotically. SyNPar is straightforward to implement and can be applied to a wide range of statistical models, including high-dimensional linear regression, generalized linear models, Cox models, and Gaussian graphical models. Through extensive simulations and real data applications, we demonstrate that SyNPar outperforms state-of-the-art methods, including knockoffs and data-splitting methods, in terms of FDR control, power, and computational efficiency.