Knockoffs for low dimensions: changing the nominal level post-hoc to gain power while controlling the FDR

Knockoffs are a powerful tool for controlled variable selection with false discovery rate (FDR) control. However, while they are frequently used in high-dimensional regressions, they lack power in low-dimensional and sparse signal settings. One of the main reasons is that knockoffs require a minimum number of selections, depending on the nominal FDR level. In this paper, we leverage e-values to allow the nominal level to be switched after looking at the data and applying the knockoff procedure. In this way, we can increase the nominal level in cases where the original knockoff procedure does not make any selections to potentially make discoveries. Also, in cases where the original knockoff procedure makes discoveries, we can often decrease the nominal level to increase the precision. These improvements come without any costs, meaning the results of our post-hoc knockoff procedure are always more informative than the results of the original knockoff procedure. Furthermore, we apply our technique to recently proposed derandomized knockoff procedures.