Debiased Front-Door Learners for Heterogeneous Effects

Abstract

In observational settings where treatment and outcome are confounded by unobserved factors but an observed mediator satisfies front-door conditions, estimating heterogeneous treatment effects remains underdeveloped. We introduce two debiased learners for heterogeneous front-door effects: FD-DR-Learner and FD-R-Learner. Both methods are constructed to be robust to nuisance estimation error, and we show they achieve fast quasi-oracle rates even when nuisance functions converge as slowly as $n^{-1/4}$. We provide error analyses that clarify their behavior under overlap and nuisance misspecification. In synthetic experiments varying sample size, nuisance noise, and overlap severity, both learners consistently outperform a plug-in baseline, with FD-R showing stronger stability under weak overlap. In a real-world case study using FARS data on primary seat-belt laws, the methods deliver reliable personalized effect estimates and interpretable heterogeneity patterns. Overall, the proposed learners offer practical and sample-efficient tools for heterogeneous causal estimation under front-door identification.