  Causal discovery from data affected by unobserved variables is an important
but difficult problem to solve. The effects that unobserved variables have on
the relationships between observed variables are more complex in nonlinear
cases than in linear cases. In this study, we focus on causal additive models
in the presence of unobserved variables. Causal additive models exhibit
structural equations that are additive in the variables and error terms. We
take into account the presence of not only unobserved common causes but also
unobserved intermediate variables. Our theoretical results show that, when the
causal relationships are nonlinear and there are unobserved variables, it is
not possible to identify all the causal relationships between observed
variables through regression and independence tests. However, our theoretical
results also show that it is possible to avoid incorrect inferences. We propose
a method to identify all the causal relationships that are theoretically
possible to identify without being biased by unobserved variables. The
empirical results using artificial data and simulated functional magnetic
resonance imaging (fMRI) data show that our method effectively infers causal
structures in the presence of unobserved variables.
