Optimal Subgroup Discovery at Every Support Threshold

arXiv (Cornell University)

Abstract

Subgroup discovery aims to identify regions of the feature space where a target variable deviates from its marginal distribution. A fundamental challenge in this problem is the trade-off between a subgroup's deviation and its support: small subgroups can be highly deviating but statistically meaningless, while large ones cannot deviate much by construction. Existing methods tackle this challenge by collapsing the two into a single scalar quality measure, implicitly committing to one particular trade-off and making it difficult to recover the most deviating subgroup under a user-specified support constraint. We instead provide the first theoretical and structural characterization of optimal subgroups with maximum Kullback-Leibler (KL) divergence under arbitrary support constraints. Under a partition-based generative model, where the feature space decomposes into regions of homogeneous conditional distributions of the target variable called atoms, we prove that every point on the deviation-support Pareto front is a union of whole atoms together with at most one fractional atom. This reduces an uncountable search to a finite combinatorial problem. Guided by this theory, we propose a simple two-step recipe: learn a homogeneous partition, then select atoms greedily. Across 19 benchmark datasets, it finds the most deviating subgroups at a range of support thresholds, and reliably improves subgroups returned by existing methods when applied as a post-processing step. These results empirically validate the sufficiency and necessity of our theoretical contributions.

Authors 6

1. Lincen Yang Aachen

   Leiden University

   Affiliation as printed

   LIACS , Leiden University , The Netherlands

2. Qi Huang Aachen

   Leiden University

   Affiliation as printed

   LIACS , Leiden University , The Netherlands

3. Bas van Stein Aachen

   Leiden University

   Affiliation as printed

   LIACS , Leiden University , The Netherlands

4. Thomas Bäck Aachen

   Leiden University

   Affiliation as printed

   LIACS , Leiden University , The Netherlands

5. Matthijs van Leeuwen Aachen

   Leiden University

   Affiliation as printed

   LIACS , Leiden University , The Netherlands

6. Zhong Li Aachen

   Leiden University · Great Bay University

   Affiliation as printed

   Great Bay University , China

   LIACS , Leiden University , The Netherlands