  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.
