The Hierarchy of Block Models
The Hierarchy of Block Models
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DOI：
10.1007/s13171-021-00247-2
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
M. Noroozi;M. Pensky
中科院分区：
文献类型：
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作者：
M. Noroozi;M. Pensky
存在各种类型的网络块模型，诸如随机块模型（SBM）、度校正块模型（DCBM）和流行度调整块模型（PABM）。虽然这导致了多种选择，但块模型没有嵌套结构。此外，从DCBM到PABM的参数数量有很大的跳跃。本文的目的是制定一个层次的块模型，不依赖于任意的可识别性条件。我们提出了一个嵌套块模型（NBM），它把SBM，DCBM和PABM作为其特定的情况下，特定的参数值，此外，允许多种版本，比DCBM更复杂，但有更少的未知参数比PABM。后者允许进行聚类和估计，而无需进行初步测试，以查看哪个块模型是真正正确的。
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.