# The Effect of Noise Level on Causal Identification with Additive Noise Models

arXiv: https://arxiv.org/abs/2108.11320 · HTML: https://mlsanity.com/paper/2108.11320/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 24 Aug 2021.

## Builds on (most cited first, 11 of 11)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexity](https://mlsanity.com/paper/1703.01196/) (2017)
- [The Recovery of Causal Poly-Trees from Statistical Data](https://mlsanity.com/paper/1304.2736/) (2013)
- [Gaussian Process Networks](https://mlsanity.com/paper/1301.3857/) (2013)
- [Information Theoretical Estimators Toolbox](https://mlsanity.com/paper/1405.2106/) (2014)
- [Score-based Causal Learning in Additive Noise Models](https://mlsanity.com/paper/1311.6359/) (2013)
- [Consistency of Causal Inference under the Additive Noise Model](https://mlsanity.com/paper/1312.5770/) (2013)
- [A direct method for estimating a causal ordering in a linear non-Gaussian acyclic model](https://mlsanity.com/paper/1408.2038/) (2014)
- [Identifiability of Gaussian Structural Equation Models with Homogeneous and Heterogeneous Error Variances](https://mlsanity.com/paper/1901.10134/) (2019)

## Abstract (arXiv)

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 in order to determine the direction of causal relationships. Many of these methods require simplifying assumptions, such as absence of confounding, cycles, and selection bias. 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. For this work, we considered bivariate cases, which is the most elementary form of a causal discovery problem where one needs to decide whether X causes Y or Y causes X, given joint distributions of two variables X, Y. Furthermore, two specific methods have been selected, textitRegression with Subsequent Independence Test and textitIdentification using Conditional Variances, which have been tested 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, the experiments in this work consider several different types of distributions as well as linear and non-linear ANMs. The results of the experiments show that these methods can fail to capture the true causal direction for some levels of noise.