Verifying formulas for interventional distributions
For researchers in causal inference, this work addresses a previously unformalized problem (verification) and provides a practical solution, though it is incremental as it builds on existing identification theory.
The paper formalizes the verification problem in causal graphical models—deciding whether a given observational formula identifies a target interventional distribution—and shows it is distinct from identification. It proposes a falsifier that yields an almost-surely correct verifier for regular exponential-family models and uses it to develop the gateway test for finding admissible sets in front-door formulas.
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.