Before revision:  It extends the ordinary ICA model in a theoretically sound and explicit way to incorporate group-wise (or environment-wise) structure in data and hence provides a justified alternative to the use of ICA on data blindly pooled across groups .
After revision:  It extends the ordinary ICA model in a theoretically sound and explicit way to incorporate group-wise (or environment-wise) confounding. We show that our general noise model allows to perform ICA in settings where other noisy ICA procedures fail. Additionally, it can be used for applications with grouped data by adjusting for different stationary noise within each group. We show that the noise model has a natural relation to causality and explain how it can be applied in the context of causal inference .