Title: Robustifying Independent Component Analysis by Adjusting for Group-Wise Stationary Noise,
Abstract: 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
this https URL.