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81
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 366 (51 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.
A p* primer: logit models for social networks
 SOCIAL NETWORKS
, 1999
"... A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others wHolland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions ..."
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Cited by 78 (1 self)
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A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others wHolland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, pp. 33–65 Ž with discussion.; Fienberg, S.E., Wasserman,
HIERARCHICAL RELATIONAL MODELS FOR DOCUMENT NETWORKS
, 2010
"... We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a fixed vocabulary. For each pair of documents, the RTM model ..."
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Cited by 50 (4 self)
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We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a fixed vocabulary. For each pair of documents, the RTM models their link as a binary random variable that is conditioned on their contents. The model can be used to summarize a network of documents, predict links between them, and predict words within them. We derive efficient inference and estimation algorithms based on variational methods that take advantage of sparsity and scale with the number of links. We evaluate the predictive performance of the RTM for large networks of scientific abstracts, web documents, and geographically tagged news.
Detecting communities and their evolutions in dynamic social networks  a Bayesian approach
 MACH LEARN
, 2010
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Stochastic blockmodels with a growing number of classes
, 2012
"... We present asymptotic and finitesample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root ..."
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Cited by 44 (11 self)
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We present asymptotic and finitesample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least polylogarithmically in this size. We also establish finitesample confidence bounds on maximumlikelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising selfreported school friendships, resulting in block estimates that reveal residual structure.
Recovering temporally rewiring networks: A modelbased approach
 in Proc. 24th Int. Conf. Machine learning
, 2007
"... A plausible representation of relational information among entities in dynamic systems such as a living cell or a social community is a stochastic network which is topologically rewiring and semantically evolving over time. While there is a rich literature on modeling static or temporally invariant ..."
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Cited by 43 (5 self)
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A plausible representation of relational information among entities in dynamic systems such as a living cell or a social community is a stochastic network which is topologically rewiring and semantically evolving over time. While there is a rich literature on modeling static or temporally invariant networks, much less has been done toward modeling the dynamic processes underlying rewiring networks, and on recovering such networks when they are not observable. We present a class of hidden temporal exponential random graph models (htERGMs) to study the yet unexplored topic of modeling and recovering temporally rewiring networks from time series of node attributes such as activities of social actors or expression levels of genes. We show that one can reliably infer the latent timespecific topologies of the evolving networks from the observation. We report empirical results on both synthetic data and a Drosophila lifecycle gene expression data set, in comparison with a static counterpart of htERGM. 1.
A STATESPACE MIXED MEMBERSHIP BLOCKMODEL FOR DYNAMIC NETWORK TOMOGRAPHY
 SUBMITTED TO THE ANNALS OF APPLIED STATISTICS
"... In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper, we propose a modelbased approach to analyze what we will refer to as the dynamic tomography of such timeevolving networks. Our approach offers an intuitive bu ..."
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Cited by 38 (1 self)
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In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper, we propose a modelbased approach to analyze what we will refer to as the dynamic tomography of such timeevolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the statespace model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a timeevolving mixed membership vector that allows actors to behave differently over time and carry out different roles/functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson’s network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors.
p2: A random effects model with covariates for directed graphs
 Statistica Neerlandica
, 2004
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