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A topic of great current interest is Causal Representation Learning (CRL),whose goal is to learn a causal model for hidden features in a data-drivenmanner. Unfortunately, CRL is severely ill-posed since it is a combination ofthe two notoriously ill-posed problems of representation learning and causaldiscovery. Yet, finding practical identifiability conditions that guarantee aunique solution is crucial for its practical applicability. Most approaches sofar have been based on assumptions on the latent causal mechanisms, such astemporal causality, or existence of supervision or interventions; these can betoo restrictive in actual applications. Here, we show identifiability based onnovel, weak constraints, which requires no temporal structure, intervention,nor weak supervision. The approach is based assuming the observational mixingexhibits a suitable grouping of the observational variables. We also propose anovel self-supervised estimation framework consistent with the model, prove itsstatistical consistency, and experimentally show its superior CRL performancescompared to the state-of-the-art baselines. We further demonstrate itsrobustness against latent confounders and causal cycles.

Causal Representation Learning Made Identifiable by Grouping of Observational Variables