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 have been developed rather independently. We observe that several methods in both representation and causal structure learning rely on the same data-generating process (DGP), namely, exchangeable but not i.i.d. (independent and identically distributed) data. We provide a unified framework, termed Identifiable Exchangeable Mechanisms (IEM), for representation and structure learning under the lens of exchangeability. IEM provides new insights that let us relax the necessary conditions for causal structure identification in exchangeable non--i.i.d. data. We also demonstrate the existence of a duality condition in identifiable representation learning, leading to new identifiability results. We hope this work will pave the way for further research in causal representation learning.