论文标题
块模型的层次结构
The Hierarchy of Block Models
论文作者
论文摘要
存在各种类型的网络模型，例如随机块模型（SBM），度校正块模型（DCBM）和受欢迎程度调整后的块模型（PABM）。尽管这导致了多种选择，但块模型没有嵌套结构。另外，从DCBM到PABM的参数数量有很大的跳跃。本文的目的是制定块模型的层次结构，该模型不依赖于任意可识别性条件。我们提出了一个嵌套模型（NBM），该模型将SBM，DCBM和PABM视为具有特定参数值的特定情况，此外，还允许多种版本比DCBM更为复杂，但比PABM少的未知参数。后者允许在没有初步测试的情况下进行聚类和估算，从而查看哪种块模型确实如此。
There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identifiability conditions. We propose a Nested Block Model (NBM) that treats the SBM, the DCBM and the PABM as its particular cases with specific parameter values, and, in addition, allows a multitude of versions that are more complicated than DCBM but have fewer unknown parameters than the PABM. The latter allows one to carry out clustering and estimation without preliminary testing, to see which block model is really true.
