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Generalized Do-Calculus Without Graphs

Abstract : Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational probability. In this framework, the primitive causal relations are encoded on a Directed Acyclic Graph (DAG), which can be limitative for some applications. In this paper, we capture causality without reference to a graph and we extend the rules of do-calculus to systems that do not possess a fixed causal ordering. For this purpose, we introduce a new framework which relies on the theory developed by Witsenhausen for multi-agent stochastic control. The mapping from graphs to so called Witsenhausen's intrinsic model is natural: the primitives of the problem are the agents' information fields; the random variables are synthesized by the agents whose strategies encode the informational constraints. All in all, our framework offers a richer language than DAGs and provides a generalized do-calculus.
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https://hal.archives-ouvertes.fr/hal-02909628
Contributor : Benjamin Heymann <>
Submitted on : Thursday, July 30, 2020 - 5:45:34 PM
Last modification on : Friday, January 15, 2021 - 5:31:05 PM
Long-term archiving on: : Tuesday, December 1, 2020 - 6:31:33 PM

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Benjamin Heymann, Michel de Lara, Jean-Philippe Chancelier. Generalized Do-Calculus Without Graphs. 2020. ⟨hal-02909628⟩

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