Detecting non-causal artifacts in multivariate linear regression models

Understand

We consider linear models where $d$ potential causes $X_1,...,X_d$ 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 $\Sigma_{XX}$ 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 $\Sigma_{XX}$.