Detecting Confounding in Multivariate Linear Models via Spectral Analysis

By Dominik Janzing, B. Schoelkopf. 2017

41 citations recorded by the source corpus.

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).

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Causal Regularization (2019, background): “The only approaches that directly estimate the strength of confounding6 from PX,Y alone we are aware of are given by [19, 14].”
Detecting non-causal artifacts in multivariate linear regression models (2018, methodology): “Also here the results are qualitatively right ( β (cid:48) and ˆ β are signiﬁcantly correlated) but with a clear tendency to under-estimate confounding, which has alerady been discussed by Janzing and Schölkopf (2017).”
Multiple Causes: A Causal Graphical View (2019, background): “Finally, this paper connects to the growing literature on multiple causal inference (Tran & Blei, 2017; Wang & Blei, 2018; Ranganath & Perotte, 2018; Heckerman, 2018; Janzing & Schölkopf, 2018).”
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…”