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

arXiv: https://arxiv.org/abs/2110.08087 · HTML: https://mlsanity.com/paper/2110.08087/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 9 of 9)

- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [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)
- [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)

## Built on by (most cited first, 1 of 1)

- [Identification of Average Causal Effects in Confounded Additive Noise Models](https://mlsanity.com/paper/2407.10014/) (2024)

## 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 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.