We introduce a nested family of Bayesian nonparametric models for network and interaction data with a hierarchical granularity structure that naturally arises through finer and coarser population labelings. In the case of network data, the structure is easily visualized by merging and shattering vertices, while respecting the edge structure. We further develop Bayesian inference procedures for the model family, and apply them to synthetic and real data. The family provides a connection of practical and theoretical interest between the Hollywood model of Crane and Dempsey, and the generalized-gamma graphex model of Caron and Fox. A key ingredient for the construction of the family is fragmentation and coagulation duality for integer partitions, and for this we develop novel duality relations that generalize those of Pitman and Dong, Goldschmidt and Martin. The duality is also crucially used in our inferential procedures.

翻译：本文提出了一类嵌套的贝叶斯非参数模型，用于处理具有层次粒度结构的网络与交互数据，这种结构通过更精细和更粗略的群体标注自然形成。对于网络数据，该结构可通过合并与分裂顶点（同时保持边结构）直观呈现。我们进一步为该模型族开发了贝叶斯推断方法，并将其应用于合成数据与真实数据。该模型族在Crane与Dempsey提出的Hollywood模型和Caron与Fox提出的广义伽马图过程模型之间建立了具有实践与理论意义的联系。构建该模型族的关键要素是整数划分的分裂与凝聚对偶性，为此我们发展了新的对偶关系，推广了Pitman以及Dong、Goldschmidt与Martin的结果。该对偶性在我们的推断方法中也起着至关重要的作用。