Correcting Confounding via Random Selection of Background Variables
This addresses the challenge of causal inference in the presence of confounding for researchers in statistics and machine learning, representing a novel method for a known bottleneck.
The paper tackles the problem of distinguishing causal influence from hidden confounding by proposing a criterion based on the stability of regression coefficients when selecting different background features, and reports that the method outperforms state-of-the-art algorithms in simulated data experiments.
We propose a method to distinguish causal influence from hidden confounding in the following scenario: given a target variable Y, potential causal drivers X, and a large number of background features, we propose a novel criterion for identifying causal relationship based on the stability of regression coefficients of X on Y with respect to selecting different background features. To this end, we propose a statistic V measuring the coefficient's variability. We prove, subject to a symmetry assumption for the background influence, that V converges to zero if and only if X contains no causal drivers. In experiments with simulated data, the method outperforms state of the art algorithms. Further, we report encouraging results for real-world data. Our approach aligns with the general belief that causal insights admit better generalization of statistical associations across environments, and justifies similar existing heuristic approaches from the literature.