Unpaired Multi-Domain Causal Representation Learning
This addresses the challenge of causal representation learning when only marginal distributions are available across domains, which is incremental as it builds on existing identifiability theory.
The paper tackles the problem of learning causally related latent variables from unpaired multi-domain data, establishing sufficient conditions for identifiability of the joint distribution and shared causal graph in a linear setup.
The goal of causal representation learning is to find a representation of data that consists of causally related latent variables. We consider a setup where one has access to data from multiple domains that potentially share a causal representation. Crucially, observations in different domains are assumed to be unpaired, that is, we only observe the marginal distribution in each domain but not their joint distribution. In this paper, we give sufficient conditions for identifiability of the joint distribution and the shared causal graph in a linear setup. Identifiability holds if we can uniquely recover the joint distribution and the shared causal representation from the marginal distributions in each domain. We transform our identifiability results into a practical method to recover the shared latent causal graph.