groupICA: Independent component analysis for grouped data

We introduce groupICA, a novel independent component analysis (ICA) algorithm which decomposes linearly mixed multivariate observations into independent components that are corrupted (and rendered dependent) by hidden group-wise confounding. 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. In addition to our theoretical framework, we explain its causal interpretation and motivation, provide an efficient estimation procedure and prove identifiability of the unmixing matrix under mild assumptions. Finally, we illustrate the performance and robustness of our method on simulated data and run experiments on publicly available EEG datasets demonstrating the applicability to real-world scenarios. We provide a scikit-learn compatible pip-installable Python package groupICA as well as R and Matlab implementations accompanied by a documentation and an audible example at https://sweichwald.de/groupICA.