Detecting confounding in multivariate linear models via spectral analysis

Dominik Janzing; Bernhard Schoelkopf

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arXiv · 1704.01430

Detecting confounding in multivariate linear models via spectral analysis

Dominik Janzing·Bernhard Schoelkopf

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Abstract

We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are due to the influence of X on Y and to what extent due to a hidden common cause (confounder) of X and Y. The method relies on concentration of measure results for large dimensions d and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of each X on Y typically has `generic orientation' relative to the eigenspaces of the covariance matrix of 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.

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Dominik Janzing, Bernhard Schoelkopf. 2017-04-05. Detecting confounding in multivariate linear models via spectral analysis. https://arxiv.org/abs/1704.01430

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