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Learning causal structure from observational data often assumes that weobserve independent and identically distributed (i.\,i.\,d) data. Thetraditional approach aims to find a graphical representation that encodes thesame set of conditional independence relationships as those present in theobserved distribution. It is known that under i.\,i.\,d assumption, even withinfinite data, there is a limit to how fine-grained a causal structure we canidentify. To overcome this limitation, recent work has explored using dataoriginating from different, related environments to learn richer causalstructure. These approaches implicitly rely on the independent causalmechanisms (ICM) principle, which postulates that the mechanism giving rise toan effect given its causes and the mechanism which generates the causes do notinform or influence each other. Thus, components of the causal model canindependently change from environment to environment. Despite its wideapplication in machine learning and causal inference, there is a lack ofstatistical formalization of the ICM principle and how it enablesidentification of richer causal structures from grouped data. Here we presentnew causal de Finetti theorems which offer a first statistical formalization ofICM principle and show how causal structure identification is possible fromexchangeable data. Our work provides theoretical justification for a broadrange of techniques leveraging multi-environment data to learn causalstructure.

Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data