# Detecting non-causal artifacts in multivariate linear regression models

arXiv: https://arxiv.org/abs/1803.00810 · HTML: https://mlsanity.com/paper/1803.00810/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2018.

## Built on by (most cited first, 16 of 16)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Causal Parrots: Large Language Models May Talk Causality But Are Not Causal](https://mlsanity.com/paper/2308.13067/) (2023)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [Can Foundation Models Talk Causality?](https://mlsanity.com/paper/2206.10591/) (2022)
- [Optimal transport for causal discovery](https://mlsanity.com/paper/2201.09366/) (2022)
- [Effective Causal Discovery under Identifiable Heteroscedastic Noise Model](https://mlsanity.com/paper/2312.12844/) (2023)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Explainable AI needs formalization](https://mlsanity.com/paper/2409.14590/) (2024)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [Pearl Causal Hierarchy on Image Data: Intricacies & Challenges](https://mlsanity.com/paper/2212.12570/) (2022)
- [Correcting Confounding via Random Selection of Background Variables](https://mlsanity.com/paper/2202.02150/) (2022)
- [Interpolation and Regularization for Causal Learning](https://mlsanity.com/paper/2202.09054/) (2022)
- [An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation](https://mlsanity.com/paper/2510.25128/) (2025)
- [A Consistent Estimator for Confounding Strength](https://mlsanity.com/paper/2211.01903/) (2022)
- [Controlling for discrete unmeasured confounding in nonlinear causal models](https://mlsanity.com/paper/2408.05647/) (2024)
- [Evaluating Bivariate Causal Statements Based on Mutual Compatibility](https://mlsanity.com/paper/2606.00278/) (2026)

## Abstract (arXiv)

We consider linear models where d potential causes X1,...,Xd are correlated with one target quantity Y and propose a method to infer whether the association is causal or whether it is an artifact caused by overfitting or hidden common causes. We employ the idea that in the former case the vector of regression coefficients has 'generic' orientation relative to the covariance matrix SigmaXX of X. Using an ICA based model for confounding, we show that both confounding and overfitting yield regression vectors that concentrate mainly in the space of low eigenvalues of SigmaXX.