Detecting non-causal artifacts in multivariate linear regression models

2018/03/02 by Dominik Janzing, Janzing, Dominik, Bernhard Schoelkopf +1 · 7 citations
Chemistry · Computer Science · Mathematics · #Blind Source Separation Techniques #Electrochemical Analysis and Applications #Neural Networks and Applications #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1803.00810

7 figures, latex

arxiv created 2018/03/02 · arxiv updated 2018/03/05

Abstract

We consider linear models where d potential causes X₁,...,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 Σ_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 Σ_XX.

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