Generalization of Pearl's Front-Door Criterion
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*)) = Σz P(z | x*) Σx 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.
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