Verifying formulas for interventional distributions
arXiv:2607.13883
The paper defines the verification problem for causal graphical models—checking whether a specific observational formula correctly identifies a target interventional distribution—and introduces a falsifier and a verifier for exponential-family models, culminating in a gateway test for front‑door admissible sets.
Abstract
We formalize verification in causal graphical models: deciding whether a given observational formula identifies a target interventional distribution. This opens a problem complementary to identification, asking not whether any identifying formula exists, but whether the given formula is identifying. We show that even sound and complete solutions to identification do not solve verification. We propose a falsifier as a first practical route forward, prove that it induces an almost-surely correct verifier for regular exponential-family models, and use the resulting verifier to develop the gateway test, which finds all sets admissible for use in a front-door formula.
Equal contribution between Leonard Henckel and Sebastian Weichwald