Inferring deterministic causal relations

TL;DR

This paper introduces a method for causal inference between two variables related by an invertible function, exploiting asymmetries in the deterministic case, supported by theoretical analysis and empirical validation.

Contribution

It demonstrates that causal direction can be inferred in deterministic settings by analyzing the dependence between the function and the cause's distribution, extending previous noise-based methods.

Findings

Method works in low noise regimes

Strong empirical results on real-world data

Theoretical link to information geometry

Abstract

We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical analysis of this method, showing that it also works in the low noise regime, and link it to information geometry. We report strong empirical results on various real-world data sets from different domains.