# Flexible Nonparametric Inference for Causal Effects under the Front-Door Model

arXiv: https://arxiv.org/abs/2312.10234 · HTML: https://mlsanity.com/paper/2312.10234/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2023.

## Built on by (most cited first, 4 of 4)

- [Coarsening Bias from Variable Discretization in Causal Functionals](https://mlsanity.com/paper/2602.22083/) (2026)
- [Controllable Generative Sandbox for Causal Inference](https://mlsanity.com/paper/2603.03587/) (2026)
- [Toward a Semiparametric Efficiency Theory under Equality Constraints in Nested Markov Models](https://mlsanity.com/paper/2608.24602/) (2026)
- [What You Observe Determines How You Identify Causal Effects: Evaluating Causal Models across Observational Views](https://mlsanity.com/paper/2609.36881/) (2026)

## Abstract (arXiv)

Evaluating causal treatment effects in observational studies requires addressing confounding. While the back-door criterion enables identification through adjustment for observed covariates, it fails in the presence of unmeasured confounding. The front-door criterion offers an alternative by leveraging variables that fully mediate the treatment effect and are unaffected by unmeasured confounders of the treatment-outcome pair. We develop novel one-step and targeted minimum loss-based estimators for both the average treatment effect and the average treatment effect on the treated under front-door assumptions. Our estimators are built on multiple parameterizations of the observed data distribution, including approaches that avoid modeling the mediator density entirely, and are compatible with flexible, machine learning-based nuisance estimation. We establish conditions for root-n consistency and asymptotic linearity by deriving second-order remainder bounds. We also develop flexible tests for assessing identification assumptions, including a doubly robust testing procedure, within a semiparametric extension of the front-door model that encodes generalized (Verma) independence constraints. We further show how these constraints can be leveraged to improve the efficiency of causal effect estimators. Simulation studies confirm favorable finite-sample performance, and real-data applications in education and emergency medicine illustrate the practical utility of our methods.