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Verifying formulas for interventional distributions

Methodology 2026-07-15 v1 Artificial Intelligence Machine Learning Machine Learning

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.

Cite

@article{arxiv.2607.13883,
  title  = {Verifying formulas for interventional distributions},
  author = {Francesco Freni and Leonard Henckel and Sebastian Weichwald},
  journal= {arXiv preprint arXiv:2607.13883},
  year   = {2026}
}

Comments

Equal contribution between Leonard Henckel and Sebastian Weichwald