Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding

Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a potentially widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset. In this paper, we show that beyond conditional independencies, unobserved confounding in this setting leaves a characteristic footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general-purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.