Verifying formulas for interventional distributions
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TL;DR — This paper formalizes "verification" in causal graphical models—deciding whether a given observational formula correctly identifies a target interventional distribution—as a problem distinct from and complementary to standard causal identification. It matters because it fills a gap in causal inference theory: checking a specific formula's validity rather than just whether some valid formula exists.
- Introduces verification as a new problem: given a formula, decide if it identifies the target interventional distribution, contrasting with identification (does any identifying formula exist).
- Shows sound-and-complete identification algorithms do not solve verification, establishing the two as genuinely separate tasks.
- Proposes a "falsifier" as a practical approach and proves it yields an almost-surely correct verifier for regular exponential-family models.
- Applies the verifier to build a "gateway test" that finds all sets admissible for use in a front-door formula.
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Verifying formulas for interventional distributions
TL;DR — This paper formalizes "verification" in causal graphical models—deciding whether a given observational formula correctly identifies a target interventional distribution—as a problem distinct from and complementary to standard causal identification. It matters because it fills a gap in causal inference theory: checking a specific formula's validity rather than just whether some valid formula exists.
- Introduces verification as a new problem: given a formula, decide if it identifies the target interventional distribution, contrasting with identification (does any identifying formula exist).
- Shows sound-and-complete identification algorithms do not solve verification, establishing the two as genuinely separate tasks.
- Proposes a "falsifier" as a practical approach and proves it yields an almost-surely correct verifier for regular exponential-family models.
- Applies the verifier to build a "gateway test" that finds all sets admissible for use in a front-door formula.