Abstract

Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other hand, may have multiple subject areas and multiple authors. We introduce a statistical model, termed the Pitman-Yor hierarchical vertex components model (PY-HVCM), that is well suited for structured interaction data. The proposed PY-HVCM effectively models complex relational data by partial pooling of local information via a latent, shared population-level distribution. The PY-HCVM is a canonical example of hierarchical vertex components models—a subfamily of models for exchangeable structured interaction-labeled networks, that is, networks invariant to interaction relabeling. Theoretical analysis and supporting simulations provide clear model interpretation, and establish global sparsity and power law degree distribution. A computationally tractable Gibbs sampling algorithm is derived for inferring sparsity and power law properties of complex networks. We demonstrate the model on both the Enron e-mail dataset and an ArXiv dataset, showing goodness of fit of the model via posterior predictive validation.

 抽象的

网络数据通常是通过一组组成元素之间的一系列结构化交互产生的。例如，电子邮件交换有一个发送者，后面可能有多个接收者。另一方面，科学文章可能有多个主题领域和多个作者。我们引入了一种统计模型，称为 Pitman-Yor 分层顶点组件模型 (PY-HVCM)，它非常适合结构化交互数据。所提出的 PY-HVCM 通过潜在的、共享的群体水平分布部分池化局部信息，有效地对复杂的关系数据进行建模。 PY-HCVM 是分层顶点组件模型的典型示例 -可交换结构化交互标记网络的模型子族，即对交互重新标记具有不变性的网络。理论分析和支持模拟提供了清晰的模型解释，并建立了全局稀疏性和幂律度分布。推导了一种计算上易于处理的吉布斯采样算法，用于推断复杂网络的稀疏性和幂律特性。我们在 Enron 电子邮件数据集和 ArXiv 数据集上演示了该模型，通过后验预测验证显示了模型的拟合优度。