Generalization of Pearl's Front-Door Criterion

TL;DR

This paper extends Pearl's front-door criterion by providing a weaker set of conditions that are sufficient for causal effect estimation, broadening its applicability in causal inference.

Contribution

It introduces a generalized, weakened set of graph-based conditions that are sufficient for front-door identification, expanding its scope beyond previous limitations.

Findings

New conditions enable broader front-door identification.

The approach generalizes Pearl's original criterion.

Expands the set of problems where front-door adjustment applies.

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.