  Independent Component Analysis (ICA) aims to recover independent latent
variables from observed mixtures thereof. Causal Representation Learning (CRL)
aims instead to infer causally related (thus often statistically dependent)
latent variables, together with the unknown graph encoding their causal
relationships. We introduce an intermediate problem termed Causal Component
Analysis (CauCA). CauCA can be viewed as a generalization of ICA, modelling the
causal dependence among the latent components, and as a special case of CRL. In
contrast to CRL, it presupposes knowledge of the causal graph, focusing solely
on learning the unmixing function and the causal mechanisms. Any impossibility
results regarding the recovery of the ground truth in CauCA also apply for CRL,
while possibility results may serve as a stepping stone for extensions to CRL.
We characterize CauCA identifiability from multiple datasets generated through
different types of interventions on the latent causal variables. As a
corollary, this interventional perspective also leads to new identifiability
results for nonlinear ICA -- a special case of CauCA with an empty graph --
requiring strictly fewer datasets than previous results. We introduce a
likelihood-based approach using normalizing flows to estimate both the unmixing
function and the causal mechanisms, and demonstrate its effectiveness through
extensive synthetic experiments in the CauCA and ICA setting.
