New Preprint Establishes Exact Correspondence Between Graph Surgery and Do-Operator in Causal Models
A new preprint, arXiv:2608.17634v1, has established a precise equivalence between graphical and functional do-operator descriptions in causal models. Focusing on deterministic acyclic structural causal models with a finite number of endogenous variables, the paper presents a main theorem stating that Graph(F^iota) equals Surg(Graph(F), T_iota). It explores how replacing target mechanisms exactly removes dependencies as achieved through graph surgery. Additionally, the study addresses scenarios where the graph includes unused arrows and characterizes conditions under which equality is maintained with the original graph G instead of Graph(F).
Key facts
- The paper formalizes the equivalence of graphical and functional do-operation descriptions.
- It focuses on deterministic acyclic structural causal models with finitely many endogenous variables.
- Main theorem: Graph(F^iota) = Surg(Graph(F), T_iota).
- Replacing target mechanisms removes exactly the dependencies removed by graph surgery.
- The paper also considers models where the graph contains unused arrows.
- It characterizes when the equality holds with the given graph G instead of Graph(F).
- The preprint is listed as arXiv:2608.17634v1, announced as new.
- The do-operator is a central concept in causal inference.
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