  We consider the problem of assessing the importance of multiple variables or
factors from a dataset when side information is available. In principle, using
side information can allow the statistician to pay attention to variables with
a greater potential, which in turn, may lead to more discoveries. We introduce
an adaptive knockoff filter, which generalizes the knockoff procedure (Barber
and Cand\`es, 2015; Cand\`es et al., 2018) in that it uses both the data at
hand and side information to adaptively order the variables under study and
focus on those that are most promising. Adaptive knockoffs controls the
finite-sample false discovery rate (FDR) and we demonstrate its power by
comparing it with other structured multiple testing methods. We also apply our
methodology to real genetic data in order to find associations between genetic
variants and various phenotypes such as Crohn's disease and lipid levels. Here,
adaptive knockoffs makes more discoveries than reported in previous studies on
the same datasets.
