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The \emph{Mixed-Membership Stochastic Blockmodel (MMSB)} is a popularframework for modeling social network relationships. It can fully exploit eachindividual node's participation (or membership) in a social structure. Despiteits powerful representations, this model makes an assumption that thedistributions of relational membership indicators between two nodes areindependent. Under many social network settings, however, it is possible thatcertain known subgroups of people may have high or low correlations in terms oftheir membership categories towards each other, and such prior informationshould be incorporated into the model. To this end, we introduce a \emph{CopulaMixed-Membership Stochastic Blockmodel (cMMSB)} where an individual Copulafunction is employed to jointly model the membership pairs of those nodeswithin the subgroup of interest. The model enables the use of various Copulafunctions to suit the scenario, while maintaining the membership's marginaldistribution, as needed, for modeling membership indicators with other nodesoutside of the subgroup of interest. We describe the proposed model and itsinference algorithm in detail for both the finite and infinite cases. In theexperiment section, we compare our algorithms with other popular models interms of link prediction, using both synthetic and real world data.

Copula Mixed-Membership Stochastic Blockmodel for Intra-Subgroup Correlations