Modifying Final Splits of Classification Tree for Fine-tuning Subpopulation Target in Policy Making

Abstract: Policymakers often use Classification and Regression Trees (CART) to partition populations based on binary outcomes and target subpopulations whose probability of the binary event exceeds a threshold. However, classic CART and knowledge distillation method whose student model is a CART (referred to as KD-CART) do not minimize the misclassification risk associated with classifying the latent probabilities of these binary events. To reduce the misclassification risk, we propose two methods, Penalized Final Split (PFS) and Maximizing Distance Final Split (MDFS). PFS incorporates a tunable penalty into the standard CART splitting criterion function. MDFS maximizes a weighted sum of distances between node means and the threshold. It can point-identify the optimal split under the unique intersect latent probability assumption. In addition, we develop theoretical result for MDFS splitting rule estimation, which has zero asymptotic risk. Through extensive simulation studies, we demonstrate that these methods predominately outperform classic CART and KD-CART in terms of misclassification error. Furthermore, in our empirical evaluations, these methods provide deeper insights than the two baseline methods.