Time-Aware Differentiable Subgroup Discovery

Subgroup Discovery (SD) seeks interpretable subsets exhibiting exceptional relationships with a target variable, but conventional SD largely treats observations as static and exceptionalness as a scalar. This is inadequate when subgroup differences emerge only during particular periods or follow distinct temporal trajectories. We introduce Time-Aware Differentiable Subgroup Discovery (TDSD), which formulates longitudinal discovery as a unified who–when–how problem: identify an interpretable subgroup, localize when its discrepancy is strongest, and characterize how that discrepancy evolves. TDSD uses differentiable soft predicates and feature-selection gates for subgroup generation and differentiable temporal boundaries for window discovery. It estimates a subgroup-specific treatment–control discrepancy trajectory and optimizes a window-aware temporal quality measure, while also supporting full-trajectory behavior discovery. Synthetic experiments evaluate subgroup, temporal-window, and temporal-behavior recovery, followed by a MIMIC-IV ICU treatment-response study. TDSD recovers informative temporal structure and substantially improves temporal localization over increasingly time-aware alternatives, while experiments also expose a remaining gap between soft optimization and exact hard-rule recovery.