Group invariance principles for causal generative models

TL;DR

This paper introduces a group theoretic framework for the independence of cause and mechanism principle, unifying various causal discovery methods and offering a general tool for analyzing data generating processes.

Contribution

It proposes a novel group theoretic approach to causal discovery that generalizes existing methods based on independence of cause and mechanism.

Findings

Provides a unified mathematical framework for causal discovery methods.

Demonstrates the applicability of group transformations in causal analysis.

Offers insights into the structure of data generating mechanisms.

Abstract

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.