  We consider the problem of estimating a particular type of linear
non-Gaussian model. Without resorting to the overcomplete Independent Component
Analysis (ICA), we show that under some mild assumptions, the model is uniquely
identified by a hybrid method. Our method leverages the advantages of
constraint-based methods and independent noise-based methods to handle both
confounded and unconfounded situations. The first step of our method uses the
FCI procedure, which allows confounders and is able to produce asymptotically
correct results. The results, unfortunately, usually determine very few
unconfounded direct causal relations, because whenever it is possible to have a
confounder, it will indicate it. The second step of our procedure finds the
unconfounded causal edges between observed variables among only those adjacent
pairs informed by the FCI results. By making use of the so-called Triad
condition, the third step is able to find confounders and their causal
relations with other variables. Afterward, we apply ICA on a notably smaller
set of graphs to identify remaining causal relationships if needed. Extensive
experiments on simulated data and real-world data validate the correctness and
effectiveness of the proposed method.
