The causal dependence in data is often characterized by Directed Acyclic
Graphical (DAG) models, widely used in many areas. Causal discovery aims to
recover the DAG structure using observational data. This paper focuses on
causal discovery with multi-variate count data. We are motivated by real-world
web visit data, recording individual user visits to multiple websites. Building
a causal diagram can help understand user behavior in transitioning between
websites, inspiring operational strategy. A challenge in modeling is user
heterogeneity, as users with different backgrounds exhibit varied behaviors.
Additionally, social network connections can result in similar behaviors among
friends. We introduce personalized Binomial DAG models to address heterogeneity
and network dependency between observations, which are common in real-world
applications. To learn the proposed DAG model, we develop an algorithm that
embeds the network structure into a dimension-reduced covariate, learns each
node's neighborhood to reduce the DAG search space, and explores the
variance-mean relation to determine the ordering. Simulations show our
algorithm outperforms state-of-the-art competitors in heterogeneous data. We
demonstrate its practical usefulness on a real-world web visit dataset.

本文研究利用多元计数数据进行因果发现，引入个性化的二项式有向无环图模型以应对用户异质性和观测之间的网络依赖关系，通过将网络结构嵌入到降维协变量中来学习所提出的有向无环图模型，并探索方差 - 均值关系以确定节点的顺序。通过模拟实验证明我们的算法在异质数据上胜过现有的竞争对手，并在实际的网页访问数据集上验证了其实用性。