Verifying formulas for interventional distributions
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 45 references that are in the map. First posted on arXiv 15 Jul 2026.
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11 of 45 references.
References · 11
- 2017Nested Markov Properties for Acyclic Directed Mixed Graphscited by 39
- 2013On the Testability of Causal Models with Latent and Instrumental Variablescited by 26
- 2015Margins of discrete Bayesian networkscited by 26
- 2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
- 2024Are Bayesian networks typically faithful?cited by 6
- 2022Variable elimination, graph reduction and efficient g-formulacited by 4
- 2022Linear-Time Algorithms for Front-Door Adjustment in Causal Graphscited by 4
- 2026Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphscited by 3
- 2024On Probabilistic and Causal Reasoning with Summation Operatorscited by 2
- 2026Deriving Complete Constraints in Hidden Variable Modelscited by 2
- 2026Complete Causal Identification from Ancestral Graphs under Selection Biascited by 1
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