Title: Stochastic block models for social network data: Inferential developments
Authors: Francesco Bartolucci - University of Perugia (Italy)
Maria Francesca Marino - University of Florence (Italy)
Silvia Pandolfi - University of Perugia (Italy) [presenting]
Abstract: Stochastic Block Models (SMBs) have known a flowering interest in the social network literature. They provide a tool for discovering communities and identifying clusters of individuals characterized by similar social behaviors. According to the SBM specification, each individual in the network belongs to one of $k$ distinct blocks, corresponding to the categories of a discrete latent variable, and the probability of observing a connection between two units only depends on their block memberships. In this framework, full maximum likelihood estimates are not achievable due to the intractability of the likelihood function. For this reason, several approximate solutions are available in the literature. These alternative approaches are mainly based on classification likelihood, composite likelihood or variational approximation. We propose a new and more efficient approximate method for estimating model parameters, which has a hybrid nature as it is based on a classification likelihood but has features in common also with full likelihood and composite likelihood inference. Moreover, it relies on an optimization algorithm with structure and numerical complexity similar to that of the variational approach, while being typically faster to converge. We illustrate the potential of the proposed approach by an intensive simulation study.