  Model-X knockoffs is a general procedure that can leverage any feature
importance measure to produce a variable selection algorithm, which discovers
true effects while rigorously controlling the number or fraction of false
positives. Model-X knockoffs is a randomized procedure which relies on the
one-time construction of synthetic (random) variables. This paper introduces a
derandomization method by aggregating the selection results across multiple
runs of the knockoffs algorithm. The derandomization step is designed to be
flexible and can be adapted to any variable selection base procedure to yield
stable decisions without compromising statistical power. When applied to the
base procedure of Janson et al. (2016), we prove that derandomized knockoffs
controls both the per family error rate (PFER) and the k family-wise error rate
(k-FWER). Further, we carry out extensive numerical studies demonstrating tight
type-I error control and markedly enhanced power when compared with alternative
variable selection algorithms. Finally, we apply our approach to multi-stage
genome-wide association studies of prostate cancer and report locations on the
genome that are significantly associated with the disease. When
cross-referenced with other studies, we find that the reported associations
have been replicated.
