  The task of subgroup discovery (SD) is to find interpretable descriptions of
subsets of a dataset that stand out with respect to a target attribute. To
address the problem of mining large numbers of redundant subgroups, subgroup
set discovery (SSD) has been proposed. State-of-the-art SSD methods have their
limitations though, as they typically heavily rely on heuristics and/or
user-chosen hyperparameters.
  We propose a dispersion-aware problem formulation for subgroup set discovery
that is based on the minimum description length (MDL) principle and subgroup
lists. We argue that the best subgroup list is the one that best summarizes the
data given the overall distribution of the target. We restrict our focus to a
single numeric target variable and show that our formalization coincides with
an existing quality measure when finding a single subgroup, but that-in
addition-it allows to trade off subgroup quality with the complexity of the
subgroup. We next propose SSD++, a heuristic algorithm for which we empirically
demonstrate that it returns outstanding subgroup lists: non-redundant sets of
compact subgroups that stand out by having strongly deviating means and small
spread.
