arXiv: Verification Framework for Causal Graphical Models Introduces 'Gateway Test' for Front-Door Formulas
Tags AI · OSS
A paper submitted July 15, 2026 by Freni, Henckel, and Weichwald formalizes the verification problem in causal graphical models: determining whether a given observational formula identifies a target interventional distribution. The authors prove that sound and complete identification algorithms do not solve verification, propose a falsifier-based verifier that is almost-surely correct for regular exponential-family models, and derive a 'gateway test' that finds all sets admissible for front-door identification.
Technical significance
This work addresses a foundational gap: practitioners often apply identification formulas (back-door, front-door) without verifying the formula's assumptions hold in their specific graph. The gateway test provides an algorithmic check for front-door validity, which could be integrated into causal discovery toolchains. The almost-sure correctness for exponential families covers most parametric models used in practice, though non-parametric or misspecified settings remain open.