Detecting Confounding in Multivariate Linear Models via Spectral Analysis

Janzing Dominik () and Schölkopf Bernhard
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Janzing Dominik: Deaprtment ‘Empirical Inference’,Max Planck Institute for Intelligent Systems,Spemannstr. 36, 70569Tübingen,Germany
Schölkopf Bernhard: Deaprtment ‘Empirical Inference’,Max Planck Institute for Intelligent Systems,Tübingen,Germany

Journal of Causal Inference, 2018, vol. 6, issue 1, 27

Abstract: We study a model where one target variable Y$Y$ is correlated with a vector X:=(X1,…,Xd)$\textbf{X}:=(X_1,\dots,X_d)$ of predictor variables being potential causes of Y$Y$. We describe a method that infers to what extent the statistical dependences between X$\textbf{X}$ and Y$Y$ are due to the influence of X$\textbf{X}$ on Y$Y$ and to what extent due to a hidden common cause (confounder) of X$\textbf{X}$ and Y$Y$. The method relies on concentration of measure results for large dimensions d$d$ and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of each X$\textbf{X}$ on Y$Y$ typically has ‘generic orientation’ relative to the eigenspaces of the covariance matrix of X$\textbf{X}$. For the special case of a scalar confounder we show that confounding typically spoils this generic orientation in a characteristic way that can be used to quantitatively estimate the amount of confounding (subject to our idealized model assumptions).

Keywords: confounding; independence of mechanisms; spectral analysis (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:causin:v:6:y:2018:i:1:p:27:n:2

DOI: 10.1515/jci-2017-0013

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