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24
Mixed membership stochastic block models for relational data with application to proteinprotein interactions
 In Proceedings of the International Biometrics Society Annual Meeting
, 2006
"... 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 authorrecipient email, and social networks. Analyzing such data with p ..."
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Cited by 182 (30 self)
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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 authorrecipient 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.
Markov Chain Monte Carlo Estimation of Exponential Random Graph Models
 Journal of Social Structure
, 2002
"... 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 MetropolisHastings sampling. The estimation procedures consider ..."
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Cited by 109 (16 self)
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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 MetropolisHastings sampling. The estimation procedures considered are based on the RobbinsMonro algorithm for approximating a solution to the likelihood equation.
Settings in social networks: A measurement model
 Sociological Methodology
, 2003
"... 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 ..."
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Cited by 12 (1 self)
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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 modelbased 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.
Conditional Maximum Likelihood Estimation under Various Specifications of Exponential Random Graph Models
 Frank. University of Stockholm: Department of Statistics
, 2002
"... This paper considers only models with such a conditioning ..."
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Cited by 12 (8 self)
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This paper considers only models with such a conditioning
A Bayesian approach toward finding communities and their evolutions in dynamic social networks
 In SDM’09: proceedings of the 2009 SIAM international
, 2009
"... 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 ..."
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Cited by 9 (1 self)
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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 reallife data demonstrate that our model achieves higher accuracy and reveals more insights in the data than several stateoftheart algorithms.
Comparing Social Networks: Size, Density, and Local Structure
"... 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 (subgraphs of th ..."
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Cited by 9 (0 self)
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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 (subgraphs 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 networklevel 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
Statistical Modeling of Network Panel Data: GoodnessofFit.” Unpublished Manuscript
, 2004
"... A popular approach to model network panel data is to embed the discrete observations of the network in a latent, continuoustime Markov process. A scoretype test statistic for goodnessoffit tests is proposed, which is useful for studying the goodnessoffit of a wide range of models. The finites ..."
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Cited by 3 (0 self)
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A popular approach to model network panel data is to embed the discrete observations of the network in a latent, continuoustime Markov process. A scoretype test statistic for goodnessoffit tests is proposed, which is useful for studying the goodnessoffit of a wide range of models. The finitesample behavior of the test statistic is evaluated by a Monte Carlo simulation study, and its usefulness is demonstrated by an application to empirical data.
Cycle Census Statistics for Exponential Random Graph Models
"... Exponential family models for random graphs (ERGs, also known as p ∗ models) are an increasingly popular tool for the analysis of social networks. ERGs allow for the parameterization of complex dependence among edges within a likelihoodbased framework, and are often used to model local influences o ..."
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Cited by 2 (2 self)
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Exponential family models for random graphs (ERGs, also known as p ∗ models) are an increasingly popular tool for the analysis of social networks. ERGs allow for the parameterization of complex dependence among edges within a likelihoodbased framework, and are often used to model local influences on global structure. This paper introduces a family of cycle statistics, which allow for the modeling of longrange dependence within ERGs. These statistics are shown to arise from a family of partial conditional dependence assumptions based on an extended form of reciprocity, here called reciprocal path dependence. Algorithms for computing cycle statistic changescores and the cycle census are provided, as are analytical expressions for the first and approximate second moments of the cycle census under a Bernoulli null model. An illustrative application of ERG modeling using cycle statistics is also provided.