Robust subgroup discovery

We introduce the problem of robust subgroup discovery, i.e., finding a set interpretable descriptions subsets that 1) stand out with respect to one or more target attributes, 2) are statistically robust, and 3) non-redundant. Many attempts have been made mine either locally subgroups tackle pattern explosion, but we first address both challenges at same time from global modelling perspective. First, formulate broad model class lists, ordered sets subgroups, for univariate multivariate targets can consist nominal numeric variables, including traditional top-1 discovery in its definition. This novel allows us formalise optimal using Minimum Description Length (MDL) principle, where resort Normalised Maximum Likelihood Bayesian encodings targets, respectively. Second, lists is NP-hard. Therefore, propose SSD++, greedy heuristic finds good guarantees most significant found according MDL criterion added each iteration. In fact, gain shown be equivalent one-sample proportion, multinomial, t-test between dataset marginal distributions plus multiple hypothesis testing penalty. Furthermore, empirically show on 54 datasets SSD++ outperforms previous methods terms quality, generalisation unseen data, list size.