A ubiquitous problem in igh-dimensional analysis is the identification of pre-defined sets that are enriched for features showing an association of interest. In this situation, inference is performed on sets, not individual features. We propose an approach which focuses on estimating the fraction of non-null features in a set. We search for unions of disjoint sets (atoms), using as the loss function a weighted average of the number of false and missed discoveries. We prove that the solution is equivalent to thresholding the atomic false discovery rate and that our approach results in a more interpretable set analysis.


Bioinformatics | Computational Biology