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The goal of causal representation learning is to find a representation ofdata that consists of causally related latent variables. We consider a setupwhere one has access to data from multiple domains that potentially share acausal representation. Crucially, observations in different domains are assumedto be unpaired, that is, we only observe the marginal distribution in eachdomain but not their joint distribution. In this paper, we give sufficientconditions for identifiability of the joint distribution and the shared causalgraph in a linear setup. Identifiability holds if we can uniquely recover thejoint distribution and the shared causal representation from the marginaldistributions in each domain. We transform our identifiability results into apractical method to recover the shared latent causal graph.

Unpaired Multi-Domain Causal Representation Learning