Generalized Do-Calculus Without Graphs.

Summary 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.