  Acyclic model, often depicted as a directed acyclic graph (DAG), has been
widely employed to represent directional causal relations among collected
nodes. In this article, we propose an efficient method to learn linear
non-Gaussian DAG in high dimensional cases, where the noises can be of any
continuous non-Gaussian distribution. This is in sharp contrast to most
existing DAG learning methods assuming Gaussian noise with additional variance
assumptions to attain exact DAG recovery. The proposed method leverages a novel
concept of topological layer to facilitate the DAG learning. Particularly, we
show that the topological layers can be exactly reconstructed in a bottom-up
fashion, and the parent-child relations among nodes in each layer can also be
consistently established. More importantly, the proposed method does not
require the faithfulness or parental faithfulness assumption which has been
widely assumed in the literature of DAG learning. Its advantage is also
supported by the numerical comparison against some popular competitors in
various simulated examples as well as a real application on the global spread
of COVID-19.
