  Linear non-Gaussian causal models postulate that each random variable is a
linear function of parent variables and non-Gaussian exogenous error terms. We
study identification of the linear coefficients when such models contain latent
variables. Our focus is on the commonly studied acyclic setting, where each
model corresponds to a directed acyclic graph (DAG). For this case, prior
literature has demonstrated that connections to overcomplete independent
component analysis yield effective criteria to decide parameter identifiability
in latent variable models. However, this connection is based on the assumption
that the observed variables linearly depend on the latent variables. Departing
from this assumption, we treat models that allow for arbitrary non-linear
latent confounding. Our main result is a graphical criterion that is necessary
and sufficient for deciding the generic identifiability of direct causal
effects. Moreover, we provide an algorithmic implementation of the criterion
with a run time that is polynomial in the number of observed variables.
Finally, we report on estimation heuristics based on the identification result,
explore a generalization to models with feedback loops, and provide new results
on the identifiability of the causal graph.
