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131
Dynamic Mixed Membership Blockmodel for Evolving Networks
"... In a dynamic social or biological environment, interactions between the underlying actors can undergo large and systematic changes. Each actor can assume multiple roles and their degrees of affiliation to these roles can also exhibit rich temporal phenomena. We propose a state space mixed membership ..."
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In a dynamic social or biological environment, interactions between the underlying actors can undergo large and systematic changes. Each actor can assume multiple roles and their degrees of affiliation to these roles can also exhibit rich temporal phenomena. We propose a state space mixed membership stochastic blockmodel which can track across time the evolving roles of the actors. We also derive an efficient variational inference procedure for our model, and apply it to the Enron email networks, and rewiring gene regulatory networks of yeast. In both cases, our model reveals interesting dynamical roles of the actors. 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.
The method of moments and degree distributions for network models
 Ann. Statist
, 2011
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Matrix estimation by universal singular value thresholding
, 2012
"... Abstract. Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially after the pioneering works of Emmanuel Candès and ..."
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Abstract. Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially after the pioneering works of Emmanuel Candès and collaborators. This paper introduces a simple estimation procedure, called Universal Singular Value Thresholding (USVT), that works for any matrix that has ‘a little bit of structure’. Surprisingly, this simple estimator achieves the minimax error rate up to a constant factor. The method is applied to solve problems related to low rank matrix estimation, blockmodels, distance matrix completion, latent space models, positive definite matrix completion, graphon estimation, and generalized Bradley–Terry models for pairwise comparison. 1.
Supplement A to “Overlapping stochastic block models with application to the French blogosphere network.” DOI: 10.12.14/10AOAS382SUPP
, 2010
"... ar ..."
H.: Graph mining applications to social network analysis
 Managing and Mining Graph Data, Advances in Database Systems
, 2010
"... ..."
Bayesian inference for exponential random graph models
 Social Networks
, 2011
"... Bayesian inference for exponential random graph models Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can be ca ..."
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Cited by 17 (4 self)
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Bayesian inference for exponential random graph models Exponential random graph models are extremely difficult models to handle from a statistical viewpoint, since their normalising constant, which depends on model parameters, is available only in very trivial cases. We show how inference can be carried out in a Bayesian framework using a MCMC algorithm, which circumvents the need to calculate the normalising constants. We use a population MCMC approach which accelerates convergence and improves mixing of the Markov chain. This approach improves performance with respect to the Monte Carlo maximum likelihood method of Geyer and Thompson (1992). 1
Community Evolution Detection in Dynamic Heterogeneous Information Networks ∗
"... As the rapid development of all kinds of online databases, huge heterogeneous information networks thus derived are ubiquitous. Detecting evolutionary communities in these networks can help people better understand the structural evolution of the networks. However, most of the current community evol ..."
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As the rapid development of all kinds of online databases, huge heterogeneous information networks thus derived are ubiquitous. Detecting evolutionary communities in these networks can help people better understand the structural evolution of the networks. However, most of the current community evolution analysis is based on the homogeneous networks, while a real community usually involves different types of objects in a heterogeneous network. For example, when referring to a research community, it contains a set of authors, a set of conferences or journals and a set of terms. In this paper, we study the problem of detecting evolutionary multityped communities defined as netclusters in dynamic heterogeneous networks. A Dirichlet Process Mixture Modelbased generative model is proposed to model the community generations. At each time stamp, a clustering of communities with the best cluster number that can best explain the current and historical networks are automatically detected. A Gibbs samplingbased inference algorithm is provided to inference the model. Also, the evolution structure can be read from the model, which can help users better understand the birth, split and death of communities. Experiments on two real datasets, namely DBLP and Delicious.com, have shown the effectiveness of the algorithm.
A Latent Space Model for Rank Data.
"... Proportional representation by means of a single transferable vote (PRSTV) is the electoral system employed in Irish elections. In this system, voters rank some or all of the candidates in order of preference. A latent space model is proposed for these election data where both candidates and voters ..."
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Proportional representation by means of a single transferable vote (PRSTV) is the electoral system employed in Irish elections. In this system, voters rank some or all of the candidates in order of preference. A latent space model is proposed for these election data where both candidates and voters are located in the same Ddimensional space. The locations are determined by the ranked preferences which are modeled using the PlackettLuce model for rank data. Voter positions reflect their preferences while the candidate locations represent the global view of the candidates by the electorate. 1.
PSEUDOLIKELIHOOD METHODS FOR COMMUNITY DETECTION IN LARGE SPARSE NETWORKS
 SUBMITTED TO THE ANNALS OF STATISTICS
, 2013
"... Many algorithms have been proposed for fitting network models with communities but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudolikelihood method for fitting the stochastic block model for networks, as well as a variant that a ..."
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Many algorithms have been proposed for fitting network models with communities but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudolikelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the example of a network of political blogs. We also propose spectral clustering with perturbations, a method of independent interest, which works well on sparse networks where regular spectral clustering fails, and use it to provide an initial value for pseudolikelihood. We prove that pseudolikelihood provides consistent estimates of the communities under a mild condition on the starting value, for the case of a block model with two balanced communities.