Differential Subgroup Discovery: Characterizing Where Two Populations Differ, and Why

arXiv cs.LG / 5/1/2026

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Key Points

The paper introduces “differential subgroups,” subsets from two populations that look similar in feature space but show unusually different outcomes.
It formulates a general optimization objective for discovering these subgroups and derives conditions under which the identified differences can be causally interpreted.
The authors propose DiffSub, a gradient-based method designed to find interpretable differential subgroups in tabular datasets.
Experiments on synthetic data and multiple real-world scenarios (medical analysis, model-error diagnostics, and treatment-effect studies) show that DiffSub can pinpoint where population gaps arise and what covariate combinations may structurally drive them.

Abstract

We study the problem of understanding where two populations differ within a feature space, which we formalize in the concept of a differential subgroup: a subset of individuals from both populations who, despite sharing similar characteristics, exhibit exceptional differences in a target outcome. Differential subgroups reveal the regions of the feature space where population-level gaps are most pronounced and can help practitioners identify the covariate combinations that are structurally responsible for these differences, e.g.~in clinical analysis, model diagnostics, or treatment-effect studies. We introduce a general optimization objective for discovering differential subgroups and establish conditions under which the resulting subgroups admit a causal interpretation of population differences. We propose DiffSub, a gradient-based approach that discovers interpretable differential subgroups in tabular data. Across synthetic benchmarks, medical case studies, model-error analyses, and treatment-effect settings, DiffSub identifies informative subgroups that reveal where population differences arise and why.