Unpaired Multi-Domain Causal Representation Learning

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 spotlightEveryoneRevisionsBibTeX
Keywords: linear structural equation models, causality, representation learning, independent component analysis, structure identifiability, multiple views, graphical model
Abstract: 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 results into a practical method to recover the shared latent causal graph.
Supplementary Material: zip
Submission Number: 5119