Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data
Abstract
Learning causal structure from observational data often assumes we observe independent and identically distributed (i.i.d.) data. It aims to find a graphical representation that encodes the same set of conditional independence relationships as those present in the observed distribution. It is known that even with unlimited data, there is a limit to how fine-grained a causal structure we can identify. To overcome this limitation of the i.i.d. setting, recent work has explored using data originating from different, related environments to learn richer causal structures. These approaches implicitly rely on the independent causal mechanisms (ICM) principle, which postulates that the mechanism giving rise to an effect given its causes and the mechanism which generates the causes do not inform or influence each other. Thus, components of the causal model can independently change from environment to environment. Despite its wide application in machine learning and causal inference, there is a lack of statistical formalization of the ICM principle and how it enables the identification of richer causal structures from grouped data. Here we present new Causal de Finetti theorems which offer the first statistical formalization of the ICM principle and show how causal structure identification is possible from exchangeable data.
