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The postulate of independence of cause and mechanism (ICM) has recently ledto several new causal discovery algorithms. The interpretation of independenceand the way it is utilized, however, varies across these methods. Our aim inthis paper is to propose a group theoretic framework for ICM to unify andgeneralize these approaches. In our setting, the cause-mechanism relationshipis assessed by comparing it against a null hypothesis through the applicationof random generic group transformations. We show that the group theoretic viewprovides a very general tool to study the structure of data generatingmechanisms with direct applications to machine learning.

Group invariance principles for causal generative models