  Many real-world decision-making tasks require learning casual relationships
between a set of variables. Typical causal discovery methods, however, require
that all variables are observed, which might not be realistic in practice.
Unfortunately, in the presence of latent confounding, recovering casual
relationships from observational data without making additional assumptions is
an ill-posed problem. Fortunately, in practice, additional structure among the
confounders can be expected, one such example being pervasive confounding,
which has been exploited for consistent causal estimation in the special case
of linear causal models. In this paper, we provide a proof and method to
estimate causal relationships in the non-linear, pervasive confounding setting.
The heart of our procedure relies on the ability to estimate the pervasive
confounding variation through a simple spectral decomposition of the observed
data matrix. We derive a DAG score function based on this insight, and
empirically compare our method to existing procedures. We show improved
performance on both simulated and real datasets by explicitly accounting for
both confounders and non-linear effects.
