  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-driven
manner. Unfortunately, CRL is severely ill-posed since it is a combination of
the two notoriously ill-posed problems of representation learning and causal
discovery. Yet, finding practical identifiability conditions that guarantee a
unique solution is crucial for its practical applicability. Most approaches so
far have been based on assumptions on the latent causal mechanisms, such as
temporal causality, or existence of supervision or interventions; these can be
too restrictive in actual applications. Here, we show identifiability based on
novel, weak constraints, which requires no temporal structure, intervention,
nor weak supervision. The approach is based on assuming the observational
mixing exhibits a suitable grouping of the observational variables. We also
propose a novel self-supervised estimation framework consistent with the model,
prove its statistical consistency, and experimentally show its superior CRL
performances compared to the state-of-the-art baselines. We further demonstrate
its robustness against latent confounders and causal cycles.
