Detecting non-causal artifacts in multivariate linear regression models

By Dominik Janzing, Bernhard Schölkopf. 2018

36 citations recorded by the source corpus.

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 $\Sigma_{XX}$.

Subfields: Artificial Intelligence, Electrochemistry, Causal Inference & Discovery, Signal Processing

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Citations in the corpus

Toward Causal Representation Learning (2021, background): “10Other dependence measures have been proposed for highdimensional linear settings and time series [28], [119], [121], [122], [126], [226].”
Towards Causal Representation Learning (2021, background): “9Other dependence measures have been proposed for high-dimensional linear settings and time series [124, 226, 27, 122, 119, 125].”
Causality for Machine Learning (2019, background): “…been proposed for high-dimensional linear settings and time series by Janzing et al. (2010); Shajarisales et al. (2015); Besserve et al. (2018a); Janzing and Schölkopf (2018), see also Janzing (2019). information; i.e., two conditionals are considered independent if knowing (the shortest…”
Causal Regularization (2019, methodology): “The only approaches that directly estimate the strength of confounding6 from PX,Y alone we are aware of are given by [19, 14].”
The Blessings of Multiple Causes (2018, background): “More recently, Sharma, Hofman, and Watts (2016) leveraged auxiliary outcome data to test for confounding; Janzing and Schölkopf (2018a; 2018b), and Liu and Chan (2018) developed tests for non-confounding in multivariate linear regression; Cinelli et al. (2019) developed sensitivity analysis for…”