Reliably learning group structures among nodes in network data is challenging
in several applications. We are particularly motivated by studying covert
networks that encode relationships among criminals. These data are subject to
measurement errors, and exhibit a complex combination of an unknown number of
core-periphery, assortative and disassortative structures that may unveil key
architectures of the criminal organization. The coexistence of these noisy
block patterns limits the reliability of routinely-used community detection
algorithms, and requires extensions of model-based solutions to realistically
characterize the node partition process, incorporate information from node
attributes, and provide improved strategies for estimation and uncertainty
quantification. To cover these gaps, we develop a new class of extended
stochastic block models (ESBM) that infer groups of nodes having common
connectivity patterns via Gibbs-type priors on the partition process. This
choice encompasses many realistic priors for criminal networks, covering
solutions with fixed, random and infinite number of possible groups, and
facilitates the inclusion of node attributes in a principled manner. Among the
new alternatives in our class, we focus on the Gnedin process as a realistic
prior that allows the number of groups to be finite, random and subject to a
reinforcement process coherent with criminal networks. A collapsed Gibbs
sampler is proposed for the whole ESBM class, and refined strategies for
estimation, prediction, uncertainty quantification and model selection are
outlined. The ESBM performance is illustrated in realistic simulations and in
an application to an Italian mafia network, where we unveil key complex block
structures, mostly hidden from state-of-the-art alternatives.

通过基于吉布斯先验的扩展随机块模型（ESBM），本文研究了包含测量误差、未知核 - 边缘、同类与异类结构的隐藏式犯罪网络的组结构学习问题，并针对各类不确定性提出了更准确的建模、估计和预测策略，其中以 Gnedin 过程为先验的 ESBM 表现出较高的准确性。