We develop a model for examining data that consists of pairwise measurements, for example, presence or absence of links between pairs of objects. Examples include protein interactions and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilistic models requires special assumptions, since the usual independence or exchangeability assumptions no longer hold. We introduce a class of latent variable models for pairwise measurements: mixed membership stochastic blockmodels. Models in this class combine a global model of dense patches of connectivity (blockmodel) and a local model to instantiate nodespecific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference. We demonstrate the advantages of mixed membership stochastic blockmodels with applications to social networks and protein interaction networks.

This paper is about estimating the parameters of the exponential random graph model, also known as the p # model, using frequentist Markov chain Monte Carlo (MCMC) methods. The exponential random graph model is simulated using Gibbs or Metropolis-Hastings sampling. The estimation procedures considered are based on the Robbins-Monro algorithm for approximating a solution to the likelihood equation.

Abstract not found

This paper considers only models with such a conditioning

A class of statistical models is proposed which aims to recover latent settings structures in social networks. Settings may be regarded as clusters of vertices. The measurement model builds on two assumptions. The observed network is assumed to be generated by hierarchically nested latent transitive structures, expressed by ultrametrics. It is assumed that expected tie strength decreases with ultrametric distance. The approach could be described as model-based clustering with an ultrametric space as the underlying metric to capture the dependence in the observations. Maximum likelihood methods as well as Bayesian methods are applied for statistical inference. Both approaches are implemented using Markov chain Monte Carlo methods. 1.

Abstract not found

Although a large body of work are devoted to finding communities in static social networks, only a few studies examined the dynamics of communities in evolving social networks. In this paper, we propose a dynamic stochastic block model for finding communities and their evolutions in a dynamic social network. The proposed model captures the evolution of communities by explicitly modeling the transition of community memberships for individual nodes in the network. Unlike many existing approaches for modeling social networks that estimate parameters by their most likely values (i.e., point estimation), in this study, we employ a Bayesian treatment for parameter estimation that computes the posterior distributions for all the unknown parameters. This Bayesian treatment allows us to capture the uncertainty in parameter values and therefore is more robust to data noise than point estimation. In addition, an efficient algorithm is developed for Bayesian inference to handle large sparse social networks. Extensive experimental studies based on both synthetic data and real-life data demonstrate that our model achieves higher accuracy and reveals more insights in the data than several state-of-theart algorithms.

This paper demonstrates limitations in usefulness of the triad census for studying similarities among local structural properties of social networks. A triad census succinctly summarizes the local structure of a network using the frequencies of sixteen isomorphism classes of triads (sub-graphs of three nodes). The empirical base for this study is a collection of 51 social networks measuring different relational contents (friendship, advice, agonistic encounters, victories in fights, dominance relations, and so on) among a variety of species (humans, chimpanzees, hyenas, monkeys, ponies, cows, and a number of bird species). Results show that, in aggregate, similarities among triad censuses of these empirical networks are largely explained by nodal and dyadic properties – the density of the network and distributions of mutual, asymmetric, and null dyads. These results remind us that the range of possible network-level properties is highly constrained by the size and density of the network and caution should be taken in interpreting higher order structural properties when they are largely explained by local network features. 1

Consider data consisting of pairwise measurements, such as presence or absence of links between pairs of objects. These data arise, for instance, in the analysis of protein interactions and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing pairwise measurements with probabilistic models requires special assumptions, since the usual independence or exchangeability assumptions no longer hold. Here we introduce a class of variance allocation models for pairwise measurements: mixed membership stochastic blockmodels. These models combine global parameters that instantiate dense patches of connectivity (blockmodel) with local parameters that instantiate node-specific variability in the connections (mixed membership). We develop a general variational inference algorithm for fast approximate posterior inference. We demonstrate the advantages of mixed membership stochastic blockmodels with applications to social networks and protein interaction networks.

In this paper, we consider the problem of community detection in directed networks by using probabilistic models. Most existing probabilistic models for community detection are either symmetric in which incoming links and outgoing links are treated equally or conditional in which only one type (i.e., either incoming or outgoing) of links is modeled. We present a probabilistic model for directed network community detection that aims to model both incoming links and outgoing links simultaneously and differentially. In particular, we introduce latent variables node productivity and node popularity to explicitly capture outgoing links and incoming links, respectively. We demonstrate the generality of the proposed framework by showing that both symmetric models and conditional models for community detection can be derived from the proposed framework as special cases, leading to better understanding of the existing models. We derive efficient EM algorithms for computing the maximum likelihood solutions to the proposed models. Extensive empirical studies verify the effectiveness of the new models as well as the insights obtained from the unified framework.