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Directed acyclic graph (DAG) models are widely used to represent causalrelationships among random variables in many application domains. This paperstudies a special class of non-Gaussian DAG models, where the conditionalvariance of each node given its parents is a quadratic function of itsconditional mean. Such a class of non-Gaussian DAG models are fairly flexibleand admit many popular distributions as special cases, including Poisson,Binomial, Geometric, Exponential, and Gamma. To facilitate learning, weintroduce a novel concept of topological layers, and develop an efficient DAGlearning algorithm. It first reconstructs the topological layers in ahierarchical fashion and then recoveries the directed edges between nodes indifferent layers, which requires much less computational cost than mostexisting algorithms in literature. Its advantage is also demonstrated in anumber of simulated examples, as well as its applications to two real-lifedatasets, including an NBA player statistics data and a cosmetic sales datacollected by Alibaba.

Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers