  Latent confounding has been a long-standing obstacle for causal reasoning
from observational data. One popular approach is to model the data using
acyclic directed mixed graphs (ADMGs), which describe ancestral relations
between variables using directed and bidirected edges. However, existing
methods using ADMGs are based on either linear functional assumptions or a
discrete search that is complicated to use and lacks computational tractability
for large datasets. In this work, we further extend the existing body of work
and develop a novel gradient-based approach to learning an ADMG with non-linear
functional relations from observational data. We first show that the presence
of latent confounding is identifiable under the assumptions of bow-free ADMGs
with non-linear additive noise models. With this insight, we propose a novel
neural causal model based on autoregressive flows for ADMG learning. This not
only enables us to determine complex causal structural relationships behind the
data in the presence of latent confounding, but also estimate their functional
relationships (hence treatment effects) simultaneously. We further validate our
approach via experiments on both synthetic and real-world datasets, and
demonstrate the competitive performance against relevant baselines.
