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.

翻译：直接圆形图(DAG)模型被广泛用来代表许多应用领域的随机变量之间的因果关系。本文研究的是非Gausian DAG模型的特殊类别,因为父母认为每个节点的有条件差异是其有条件平均值的二次函数。这种非Gausian DAG模型的类别相当灵活,并承认许多流行的分布为特殊案例,包括Poisson、Binomial、几何、Excential和Gamma。为了便利学习,我们引入了一个新的表层概念,并开发了一个高效的DAG学习算法。它首先以等级方式重建表层层层,然后收回不同层节点之间的定向边缘,这比文献中大多数现有的算法要少得多。它的优势还体现在一些模拟的例子中,以及对两个真实生活数据集的应用,包括NBA播放器的统计数据和Alibaba收集的化妆品销售数据。