  Controlled variable selection is an important analytical step in various
scientific fields, such as brain imaging or genomics. In these high-dimensional
data settings, considering too many variables leads to poor models and high
costs, hence the need for statistical guarantees on false positives. Knockoffs
are a popular statistical tool for conditional variable selection in high
dimension. However, they control for the expected proportion of false
discoveries (FDR) and not their actual proportion (FDP). We present a new
method, KOPI, that controls the proportion of false discoveries for
Knockoff-based inference. The proposed method also relies on a new type of
aggregation to address the undesirable randomness associated with classical
Knockoff inference. We demonstrate FDP control and substantial power gains over
existing Knockoff-based methods in various simulation settings and achieve good
sensitivity/specificity tradeoffs on brain imaging and genomic data.
