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We introduce coroICA, confounding-robust independent component analysis, anovel ICA algorithm which decomposes linearly mixed multivariate observationsinto independent components that are corrupted (and rendered dependent) byhidden group-wise stationary confounding. It extends the ordinary ICA model ina theoretically sound and explicit way to incorporate group-wise (orenvironment-wise) confounding. We show that our proposed general noise modelallows to perform ICA in settings where other noisy ICA procedures fail.Additionally, it can be used for applications with grouped data by adjustingfor different stationary noise within each group. Our proposed noise model hasa natural relation to causality and we explain how it can be applied in thecontext of causal inference. In addition to our theoretical framework, weprovide an efficient estimation procedure and prove identifiability of theunmixing matrix under mild assumptions. Finally, we illustrate the performanceand robustness of our method on simulated data, provide audible and visualexamples, and demonstrate the applicability to real-world scenarios byexperiments on publicly available Antarctic ice core data as well as two EEGdata sets. We provide a scikit-learn compatible pip-installable Python packagecoroICA as well as R and Matlab implementations accompanied by a documentationat https://sweichwald.de/coroICA/

Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise