Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning

Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields developed rather independently. We observe that several structure and representation identifiability methods, particularly those that require multiple environments, rely on exchangeable non-i.i.d. (independent and identically distributed) data. To formalize this connection, we propose the Identifiable Exchangeable Mechanisms (IEM) framework to unify key representation and causal structure learning methods. IEM provides a unified probabilistic graphical model encompassing causal discovery, Independent Component Analysis, and Causal Representation Learning. With the help of the IEM model, we generalize the Causal de Finetti theorem of Guo et al. (2024a) by relaxing the necessary conditions for causal structure identification in exchangeable data. We term these conditions cause and mechanism variability, and show how they imply a duality condition in identifiable representation learning, leading to new identifiability results.