Abstract

Directed acyclic graph (DAG) models are widely used to represent casual relationships among random variables in many application domains. This article 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 recovers 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. Supplementary materials for this article are available online.

摘要

有向无环图 (DAG) 模型被广泛用于表示许多应用领域中随机变量之间的因果关系。本文研究一类特殊的非高斯 DAG 模型，其中给定其父节点的每个节点的条件方差是其条件均值的二次函数。此类非高斯 DAG 模型相当灵活，可以将许多流行分布作为特例，包括泊松分布、二项分布、几何分布、指数分布和伽玛分布。为了便于学习，我们引入了拓扑层的新概念，并开发了一种高效的 DAG 学习算法。它首先以分层方式重建拓扑层，然后恢复不同层中节点之间的有向边，这比文献中的大多数现有算法需要更少的计算成本。它的优势也体现在一些模拟的例子中，以及它在两个现实生活中的数据集的应用，包括 NBA 球员统计数据和阿里巴巴收集的化妆品销售数据。本文的补充材料可在线获取。