Analysis of cause-effect inference by comparing regression errors

TL;DR

This paper proposes a simple causal inference method based on comparing regression errors in both directions, effective under certain assumptions, and validated on artificial and real data.

Contribution

It introduces an easy-to-implement algorithm for cause-effect inference using regression error comparison, grounded in theoretical assumptions about independence and deterministic relations.

Findings

The method accurately infers causal direction in simulated data.

It performs competitively with existing causal inference techniques.

The approach is applicable to real-world datasets with promising results.

Abstract

We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause and effect, the conditional noise distribution, and the distribution of the cause, we show that the errors are smaller in causal direction if both variables are equally scaled and the causal relation is close to deterministic. Based on this, we provide an easily applicable algorithm that only requires a regression in both possible causal directions and a comparison of the errors. The performance of the algorithm is compared with various related causal inference methods in different artificial and real-world data sets.