# Analysis of cause-effect inference by comparing regression errors

arXiv: https://arxiv.org/abs/1802.06698 · HTML: https://mlsanity.com/paper/1802.06698/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2018.

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

- [On the Role of Entropy-based Loss for Learning Causal Structures with Continuous Optimization](https://mlsanity.com/paper/2106.02835/) (2021)
- [Improving Data-driven Heterogeneous Treatment Effect Estimation Under Structure Uncertainty](https://mlsanity.com/paper/2206.12689/) (2022)

## Abstract (arXiv)

We address the problem of inferring the causal direction between two variables by comparing the least-squares errors of the predictions in both possible directions. Under the assumption of an independence between the function relating cause and effect, the conditional noise distribution, and the distribution of the cause, we show that the errors are smaller in causal direction if both variables are equally scaled and the causal relation is close to deterministic. Based on this, we provide an easily applicable algorithm that only requires a regression in both possible causal directions and a comparison of the errors. The performance of the algorithm is compared with various related causal inference methods in different artificial and real-world data sets.