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The task of subgroup discovery (SD) is to find interpretable descriptions ofsubsets of a dataset that stand out with respect to a target attribute. Toaddress the problem of mining large numbers of redundant subgroups, subgroupset discovery (SSD) has been proposed. State-of-the-art SSD methods have theirlimitations though, as they typically heavily rely on heuristics and/oruser-chosen hyperparameters.  We propose a dispersion-aware problem formulation for subgroup set discoverythat is based on the minimum description length (MDL) principle and subgrouplists. We argue that the best subgroup list is the one that best summarizes thedata given the overall distribution of the target. We restrict our focus to asingle numeric target variable and show that our formalization coincides withan existing quality measure when finding a single subgroup, but that-inaddition-it allows to trade off subgroup quality with the complexity of thesubgroup. We next propose SSD++, a heuristic algorithm for which we empiricallydemonstrate that it returns outstanding subgroup lists: non-redundant sets ofcompact subgroups that stand out by having strongly deviating means and smallspread.

Discovering outstanding subgroup lists for numeric targets using MDL