On model identifiability in analytic postnonlinear ICA

An important aspect of successfully analyzing data with blind source separation is to know the indeterminacies of the problem, that is how the separating model is related to the original mixing model. If linear independent component analysis (ICA) is used, it is well-known that the mixing matrix can be found in principle, but for more general settings not many results exist. In this work, only considering random variables with bounded densities, we prove identifiability of the postnonlinear mixing model with analytic nonlinearities and calculate its indeterminacies. A simulation confirms these theoretical findings.