Copula Mixed-Membership Stochastic Blockmodel

Abstract

The Mixed-Membership Stochastic Blockmodels (MMSB) is a popular framework for modelling social relationships by fully exploiting each individual node's participation (or membership) in a social network. Despite its powerful representations, MMSB assumes that the membership indicators of each pair of nodes (i.e., people) are distributed independently. However, such an assumption often does not hold in real-life social networks, in which certain known groups of people may correlate with each other in terms of factors such as their membership categories. To expand MMSB's ability to model such dependent relationships, a new framework - a Copula Mixed-Membership Stochastic Blockmodel - is introduced in this paper for modeling intra-group correlations, namely an individual Copula function jointly models the membership pairs of those nodes within the group of interest. This framework enables various Copula functions to be used on demand, while maintaining the membership indicator's marginal distribution needed for modelling membership indicators with other nodes outside of the group of interest. Sampling algorithms for both the finite and infinite number of groups are also detailed. Our experimental results show its superior performance in capturing group interactions when compared with the baseline models on both synthetic and real world datasets.