The Effect of Noise Level on the Accuracy of Causal Discovery Methods with Additive Noise Models

In recent years a lot of research was conducted within the area of causal inference and causal learning. Many methods were developed to identify the cause-effect pairs. These methods also proved their ability to successfully determine the direction of causal relationships from observational real-world data. Yet in bivariate situations, causal discovery problems remain challenging. A class of 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 consider a bivariate case and two specific methods Regression with Subsequent Independence Test and Identification using Conditional Variances. We perform a set of experiments with an exhaustive range of ANMs where the additive noises’ levels gradually change from 1% to 10000% of the causes’ noise level (the latter remains fixed). Additionally,
we consider several different types of distributions as well as linear and non-linear ANMs. The results of the experiments show that these causal discovery methods can fail to capture the true causal direction for some levels of noise.