Generalization of Pearl's Front-Door Criterion
Statistics Theory
2026-04-17 v1 Statistics Theory
Abstract
Pearl's front-door criterion provides a set of sufficient conditions for estimating the total causal effect from observational data in the presence of latent confounding, using the functional P(y | do(x := x*)) = \sum_z P(z | x*) \sum_x P(y | x, z) P(x). An open question is whether these conditions can be generalized to be both necessary and sufficient for the validity of this functional, similar to the generalization achieved for the back-door adjustment criterion by Shpitser. In this paper, we present a new, weakened set of graph-based conditions sufficient for the front-door formula to estimate the total causal effect, expanding the scope of problems amenable to front-door identification.
Keywords
Cite
@article{arxiv.2604.15288,
title = {Generalization of Pearl's Front-Door Criterion},
author = {Carol Wu and Elina Robeva},
journal= {arXiv preprint arXiv:2604.15288},
year = {2026}
}