网络独立性结构的层次模型
Hierarchical Models for Independence Structures of Networks
摘要：
我们引入了一系列新的网络模型，称为分层网络模型，它使我们能够以显式的方式表示网络的二元组（随机联系）之间的随机依赖性。特别是，这个家族的每个成员都可以与一个图形模型相关联，该图形模型定义了网络的二元组之间的条件独立子句，称为依赖图。每一个具有并元独立性假设的网络模型都可以推广到这个新的网络族中。使用这个新的框架，我们推广的Erdös-Rényi和beta模型，创建分层的Erdös-Rényi和beta模型。我们描述了各种方法的参数估计以及模型与稀疏依赖图的模拟研究。
英文摘要：
We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erdös-Rényi and beta-models to create hierarchical Erdös-Rényi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
