Causal Inference with Heteroscedastic Noise Models

Abstract. We study the problem of identifying the cause and the effect between two univariate continuous variables $$X$$ and $$Y$$. The examined data is purely observational, hence it is required to make assumptions about the underlying model. Often, the independence of the noise from the cause is assumed, which is not always the case for real world data. In view of this, we present a new method, which explicitly models heteroscedastic noise. With our Hec algorithm, we can find the optimal model regularized, by an information theoretic score. In thorough experiments we show, that our ability to model heteroscedastic noise translates into a superior performance on a wide range of synthetic and real-world datasets.

## Implementation

the Python source code (December 2021) by Sascha Xu.

## Related Publications

 Xu, S, Marx, A, Mian, O & Vreeken, J Causal Inference with Heteroscedastic Noise Models. In: Proceedings of the AAAI Workshop on Information Theoretic Causal Inference and Discovery (ITCI'22), 2022. Mian, OA, Marx, A & Vreeken, J Discovering Fully Oriented Causal Networks. In: Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), AAAI, 2021. (21.3% acceptance) Marx, A & Vreeken, J Identifiability of Cause and Effect using Regularized Regression. In: Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), ACM, 2019. (oral presentation 9.2% acceptance rate; overall 14.2%)