Causal Identification with Additive Noise Models: Quantifying the Effect of Noise

TL;DR

This paper empirically investigates how varying levels of additive noise affect the ability of Additive Noise Models to correctly identify causal directions in bivariate data, revealing potential limitations.

Contribution

It provides a systematic empirical analysis of the impact of noise levels on ANM-based causal inference methods, which was previously underexplored.

Findings

ANMs can fail to identify causal direction at certain noise levels

Performance varies with different distribution types and model linearity

High noise levels can obscure causal signals

Abstract

In recent years, a lot of research has been conducted within the area of causal inference and causal learning. Many methods have been developed to identify the cause-effect pairs in models and have been successfully applied to observational real-world data to determine the direction of causal relationships. Yet in bivariate situations, causal discovery problems remain challenging. One class of such methods, that also allows tackling the bivariate case, is based on Additive Noise Models (ANMs). Unfortunately, one aspect of these methods has not received much attention until now: what is the impact of different noise levels on the ability of these methods to identify the direction of the causal relationship. This work aims to bridge this gap with the help of an empirical study. We test Regression with Subsequent Independence Test (RESIT) using an exhaustive range of models where the level of additive noise gradually changes from 1\% to 10000\% of the causes' noise level (the latter remains fixed). Additionally, the experiments in this work consider several different types of distributions as well as linear and non-linear models. The results of the experiments show that ANMs methods can fail to capture the true causal direction for some levels of noise.