Ensembles of networks arise in various fields where multiple independent networks are observed on the same set of nodes, for example, a collection of brain networks constructed on the same brain regions for different individuals. However, there are few models that describe both the variations and characteristics of networks in an ensemble at the same time. In this paper, we propose to model the ensemble of networks using a Dirichlet Process Mixture of Exponential Random Graph Models (DPM-ERGMs), which divides the ensemble into different clusters and models each cluster of networks using a separate Exponential Random Graph Model (ERGM). By employing a Dirichlet process mixture, the number of clusters can be determined automatically and changed adaptively with the data provided. Moreover, in order to perform full Bayesian inference for DPM-ERGMs, we employ the intermediate importance sampling technique inside the Metropolis-within-slice sampling scheme, which addressed the problem of sampling from the intractable ERGMs on an infinite sample space. We also demonstrate the performance of DPM-ERGMs with both simulated and real datasets.
翻译:在不同的领域出现网络组合,在同一个节点上观测到多个独立的网络,例如,收集在同一脑区域为不同个人建造的脑网络,然而,很少有模型可以同时描述一个组合的网络的变异和特点,在本文中,我们提议用一个Drichlet进程集成随机图模型(DPM-ERGMs)来模拟网络的组合,将组合分成不同的组群和每个网络群群群,使用一个单独的Excential随机图模型(ERGM),通过使用一个Drichlet进程混合,可以自动确定组群的数量,并根据所提供的数据进行调整。此外,为了对DPM-ERGMs进行全面的猜想,我们采用了大都会热点中性取样技术,该方法解决了在无限样本空间从精密的ERGMs取样中取样的问题。我们还用模拟数据和真实数据显示DPM-ERGMs的性能。