  Continuous improvement in medical imaging techniques allows the acquisition
of higher-resolution images. When these are used in a predictive setting, a
greater number of explanatory variables are potentially related to the
dependent variable (the response). Meanwhile, the number of acquisitions per
experiment remains limited. In such high dimension/small sample size setting,
it is desirable to find the explanatory variables that are truly related to the
response while controlling the rate of false discoveries. To achieve this goal,
novel multivariate inference procedures, such as knockoff inference, have been
proposed recently. However, they require the feature covariance to be
well-defined, which is impossible in high-dimensional settings. In this paper,
we propose a new algorithm, called Ensemble of Clustered Knockoffs, that allows
to select explanatory variables while controlling the false discovery rate
(FDR), up to a prescribed spatial tolerance. The core idea is that
knockoff-based inference can be applied on groups (clusters) of voxels, which
drastically reduces the problem's dimension; an ensembling step then removes
the dependence on a fixed clustering and stabilizes the results. We benchmark
this algorithm and other FDR-controlling methods on brain imaging datasets and
observe empirical gains in sensitivity, while the false discovery rate is
controlled at the nominal level.
