# Error Asymmetry in Causal and Anticausal Regression

arXiv: https://arxiv.org/abs/1610.03263 · HTML: https://mlsanity.com/paper/1610.03263/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2016.

## Built on by (most cited first, 2 of 2)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Causal versions of Maximum Entropy and Principle of Insufficient Reason](https://mlsanity.com/paper/2102.03906/) (2021)

## Abstract (arXiv)

It is generally difficult to make any statements about the expected prediction error in an univariate setting without further knowledge about how the data were generated. Recent work showed that knowledge about the real underlying causal structure of a data generation process has implications for various machine learning settings. Assuming an additive noise and an independence between data generating mechanism and its input, we draw a novel connection between the intrinsic causal relationship of two variables and the expected prediction error. We formulate the theorem that the expected error of the true data generating function as prediction model is generally smaller when the effect is predicted from its cause and, on the contrary, greater when the cause is predicted from its effect. The theorem implies an asymmetry in the error depending on the prediction direction. This is further corroborated with empirical evaluations in artificial and real-world data sets.