The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed by perturbing it with random group transformations. We show that the group theoretic view encompasses previous ICM approaches and provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning.
This work introduces the concept of genericity of a cause-mechanism pair. This provides a general framework to measure of independence of mechanisms, which we apply to latent variable models. As a consequence, this framework allows to perform model selection in the context of unsupervised learning.