Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs
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Abstract (arXiv)
The do-calculus defines a general system of inference for interventional queries, allowing causal quantities to be transformed through successive applications of its rules. This process induces a rich space of equivalent interventional expressions, but combining and ordering these rules remains challenging. In this work, we introduce derivation graphs, which represent how do-calculus rules are applied and combined, and characterize the full space of observational and interventional probabilities which are equivalent under the do-calculus. The structure of these graphs yields a simple procedure that uses at most four applications of do-calculus rules. Finally, we show how applying identification algorithms to equivalent causal queries produces multiple valid estimands for the same causal quantity, eventually yielding more efficient estimators.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 9 of its 29 references that are in the map. First posted on arXiv 2 Jun 2026.
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9 of 29 references.
References · 9
- 2013On the Logic of Causal Modelscited by 19
- 2021Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variablescited by 16
- 2023DiscoBAX: Discovery of Optimal Intervention Sets in Genomic Experiment Designcited by 12
- 2018Enhancing Identification of Causal Effects by Pruningcited by 7
- 2018Simplifying Probabilistic Expressions in Causal Inferencecited by 6
- 2024Efficient adjustment for complex covariates: Gaining efficiency with DOPEcited by 5
- 2025Causal Inference with the Napkin Graphcited by 5
- 2022Efficient Real-world Testing of Causal Decision Making via Bayesian Experimental Design for Contextual Optimisationcited by 3
- 2022A note on efficient minimum cost adjustment sets in causal graphical modelscited by 2
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Citing papers per year: 2026: 3.
3 papers.