Cross-validating causal discovery via Leave-One-Variable-Out

arXiv:2411.05625v2 Announce Type: replace-cross Abstract: We propose a new approach to falsify causal discovery algorithms without ground truth, which is based on testing the causal model on a variable pair excluded during learning the causal model. Specifically, given data on X, Y, oldsymbol{Z}=X, Y, Z_1,ots,Z_k, we apply the causal discovery algorithm separately to the 'leave-one-out' data sets X, oldsymbol{Z} and Y, oldsymbol{Z}. We demonstrate that the two resulting causal models, in the form DAGs, ADMGs, CPDAGs or PAGs, often entail conclusions on the dependencies between X and Y and allow to estimate E(Ymid X=x) without any joint observations of X and Y, given only the leave-one-out datasets. This estimation is called "Leave-One-Variable-Out (LOVO)" prediction. Its error can be estimated since the joint distribution P(X, Y) is available, and X and Y have only been omitted for the purpose of falsification. We present two variants of LOVO prediction: One graphical method, which is applicable to general causal discovery algorithms, and one version tailored towards algorithms relying on specific a priori assumptions, such as linear additive noise models. Simulations indicate that the LOVO prediction error is indeed correlated with the accuracy of the causal outputs, affirming the method's effectiveness.

Source: arXiv cs.LG | 2026-08-25