Group invariance principles for causal generative models
This work addresses the need for a unified theoretical foundation in causal discovery for researchers and practitioners, though it appears incremental as it builds on existing ICM principles.
The authors tackled the problem of unifying and generalizing causal discovery algorithms based on the independence of cause and mechanism (ICM) by proposing a group theoretic framework, showing it provides a general tool for studying data generating mechanisms with applications to machine learning.
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 comparing it against a null hypothesis through the application of random generic group transformations. We show that the group theoretic view provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning.