  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.
