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Causal inference concerns the identification of cause-effect relationshipsbetween variables, e.g. establishing whether a stimulus affects activity in acertain brain region. The observed variables themselves often do not constitutemeaningful causal variables, however, and linear combinations need to beconsidered. In electroencephalographic studies, for example, one is notinterested in establishing cause-effect relationships between electrode signals(the observed variables), but rather between cortical signals (the causalvariables) which can be recovered as linear combinations of electrode signals.  We introduce MERLiN (Mixture Effect Recovery in Linear Networks), a family ofcausal inference algorithms that implement a novel means of constructing causalvariables from non-causal variables. We demonstrate through application to EEGdata how the basic MERLiN algorithm can be extended for application todifferent (neuroimaging) data modalities. Given an observed linear mixture, thealgorithms can recover a causal variable that is a linear effect of anothergiven variable. That is, MERLiN allows us to recover a cortical signal that isaffected by activity in a certain brain region, while not being a direct effectof the stimulus. The Python/Matlab implementation for all presented algorithmsis available on https://github.com/sweichwald/MERLiN

MERLiN: Mixture Effect Recovery in Linear Networks