Policy-Oriented Binary Classification: Improving (KD-)CART Final Splits for Subpopulation Targeting

Policymakers often use recursive binary split rules to partition populations based on binary outcomes and target subpopulations whose probability of this adverse binary event exceeds a threshold. We call such problems Latent Probability Classification (LPC). Practitioners typically employ Classification and Regression Trees (CART) for LPC. We prove that, in the context of LPC, classic CART and the knowledge distillation method, in which the student model is a CART (referred to as KD-CART), are suboptimal. We propose Maximizing Distance Final Split (MDFS), which generates split rules that strictly dominate CART/KD-CART under the unique intersect assumption. Under this assumption, MDFS identifies the unique best split rule. Consequently, it targets more vulnerable subpopulations than CART/KD-CART, where ``more vulnerable'' is defined as a higher probability of the adverse binary event. To further relax the assumption, we propose Penalized Final Split (PFS) and weighted Empirical risk Final Split (wEFS). Through extensive simulation studies, we demonstrate that the proposed methods predominantly outperform CART/KD-CART using two risk metrics. When applied to real-world datasets, MDFS generates policies that target more vulnerable subpopulations than the CART/KD-CART.