MERLiN: Mixture Effect Recovery in Linear Networks

Sebastian Weichwald, Moritz Grosse-Wentrup, Arthur Gretton

Abstract:

Causal inference concerns the identification of
cause-effect relationships between variables, e. g. establishing
whether a stimulus affects activity in a certain brain region. The
observed variables themselves often do not constitute meaningful
causal variables, however, and linear combinations need to be
considered. In electroencephalographic studies, for example, one
is not interested in establishing cause-effect relationships between
electrode signals (the observed variables), but rather between
cortical signals (the causal variables) which can be recovered as
linear combinations of electrode signals.
We introduce MERLiN (Mixture Effect Recovery in Linear
Networks), a family of causal inference algorithms that im-
plement a novel means of constructing causal variables from
non-causal variables. We demonstrate through application to
EEG data how the basic MERLiN algorithm can be extended
for application to different (neuroimaging) data modalities.
Given an observed linear mixture, the algorithms can recover
a causal variable that is a linear effect of another given vari-
able. That is, MERLiN allows us to recover a cortical signal
that is affected by activity in a certain brain region, while
not being a direct effect of the stimulus. The Python/Matlab
implementation for all presented algorithms is available on
https://github.com/sweichwald/MERLiN.