# Debiased Front-Door Learners for Heterogeneous Effects

arXiv: https://arxiv.org/abs/2509.22531 · HTML: https://mlsanity.com/paper/2509.22531/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Combining T-learning and DR-learning: a framework for oracle-efficient estimation of causal contrasts](https://mlsanity.com/paper/2402.01972/) (2024)
- [Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder](https://mlsanity.com/paper/2310.01937/) (2023)
- [A Neural Mean Embedding Approach for Back-door and Front-door Adjustment](https://mlsanity.com/paper/2210.06610/) (2022)
- [Causal effects of intervening variables in settings with unmeasured confounding](https://mlsanity.com/paper/2305.00349/) (2023)

## Built on by (most cited first, 2 of 2)

- [What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Views](https://mlsanity.com/paper/2609.36881/) (2026)
- [Proximal Balancing for Causal Effect Estimation under Unmeasured Confounding](https://mlsanity.com/paper/2609.40051/) (2026)

## Abstract (arXiv)

In observational settings where treatment and outcome share unmeasured confounders but an observed mediator remains unconfounded, the front-door (FD) adjustment identifies causal effects through the mediator. We study the heterogeneous treatment effect (HTE) under FD identification and introduce two debiased learners: FD-DR-Learner and FD-R-Learner. Under explicit sample-splitting, bounded-overlap, moment, and stage-learning assumptions, we show that FD-DR satisfies a product-error bound and FD-R satisfies a stage-error decomposition; these results yield conditional quasi-oracle corollaries when the relevant nuisance remainders are no larger than the target or stage oracle terms. We provide error analyses establishing this debiasedness and demonstrate robust empirical performance in synthetic studies and a real-world case study of primary seat-belt laws using Fatality Analysis Reporting System (FARS) dataset. Together, these results indicate that the proposed learners can deliver reliable and sample-efficient HTE estimates in FD scenarios when the stated assumptions are credible. The implementation is available at https://github.com/yonghanjung/FD-CATE.