  Directed acyclic graph (DAG) models are widely used to represent causal
relationships among random variables in many application domains. This paper
studies a special class of non-Gaussian DAG models, where the conditional
variance of each node given its parents is a quadratic function of its
conditional mean. Such a class of non-Gaussian DAG models are fairly flexible
and admit many popular distributions as special cases, including Poisson,
Binomial, Geometric, Exponential, and Gamma. To facilitate learning, we
introduce a novel concept of topological layers, and develop an efficient DAG
learning algorithm. It first reconstructs the topological layers in a
hierarchical fashion and then recoveries the directed edges between nodes in
different layers, which requires much less computational cost than most
existing algorithms in literature. Its advantage is also demonstrated in a
number of simulated examples, as well as its applications to two real-life
datasets, including an NBA player statistics data and a cosmetic sales data
collected by Alibaba.
