Silver Linings: On the Types of Distribution Shifts that Enhance Identifiability in Causal Representation Learning

Causal representation learning seeks to uncover latent causal variables and their relationships from observed, unstructured data, but often struggles with identifiability. While distribution shifts in traditional machine learning are seen as challenges to model reliability, they can instead act as natural interventions, introducing the variability needed to address identifiability in causal representation learning. In this paper, we introduce a non-parametric condition that characterizes the types of distribution shifts capable of enhancing identifiability within latent additive noise models. We further establish partial identifiability results when only a subset of distribution shifts satisfies this condition. Extending our analysis, we demonstrate its applicability to latent post-nonlinear causal models. Building on these theoretical insights, we propose a novel algorithm designed to learn reliable latent causal representations. Our algorithm, grounded in our theoretical findings, consistently achieves state-of-the-art performance across diverse synthetic and real-world datasets. These empirical results not only validate our theoretical contributions but also underscore the practical utility of leveraging distribution shifts to address identifiability challenges.

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Submitted to International Conference on Machine Learning (ICML) 2025