Verifying formulas for interventional distributions

Francesco Freni; Leonard Henckel; Sebastian Weichwald

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arXiv · 2607.13883

Verifying formulas for interventional distributions

Francesco Freni·Leonard Henckel·Sebastian Weichwald

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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.

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stat.ME cs.AI cs.LG stat.ML

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Francesco Freni, Leonard Henckel, Sebastian Weichwald. 2026-07-15. Verifying formulas for interventional distributions. https://arxiv.org/abs/2607.13883

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