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 URL
We introduce coroICA, confounding-robust independent component analysis , a novel ICA algorithm which decomposes linearly mixed multivariate observations into independent components that are corrupted (and rendered dependent) by hidden group-wise stationary confounding. 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 . In addition to our theoretical framework, we 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 , provide audible and visual examples, and demonstrate the applicability to real-world scenarios by experiments on publicly available Antarctic ice core data as well as two EEG data sets . We provide a scikit-learn compatible pip-installable Python package coroICA as well as R and Matlab implementations accompanied by a documentation at URL
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groupICA, a novel
coroICA, confounding-robust
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(ICA )
, a novel ICA
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stationary
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structure in data and hence provides a justified alternative to the use of ICA on data blindly pooled across groups
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
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explain its causal interpretation and motivation,
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and run experiments on publicly available EEG datasets demonstrating
, provide audible and visual examples, and demonstrate
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by experiments on publicly available Antarctic ice core data as well as two EEG data sets
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groupICA
coroICA
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and an audible example