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.

Relational clustering has attracted more and more attention due to its phenomenal impact in various important applications which involve multi-type interrelated data objects, such as Web mining, search marketing, bioinformatics, citation analysis, and epidemiology. In this paper, we propose a probabilistic model for relational clustering, which also provides a principal framework to unify various important clustering tasks including traditional attributes-based clustering, semi-supervised clustering, co-clustering and graph clustering. The proposed model seeks to identify cluster structures for each type of data objects and interaction patterns between different types of objects. Under this model, we propose parametric hard and soft relational clustering algorithms under a large number of exponential family distributions. The algorithms are applicable to relational data of various structures and at the same time unifies a number of stat-of-the-art clustering algorithms: co-clustering algorithms, the k-partite graph clustering, and semi-supervised clustering based on hidden Markov random fields.

There has been an explosive growth of data-mining models involving latent structure for clustering and classification. While having related objectives these models use different parameterizations and often very different specifications and constraints. Model choice is thus a major methodological issue and a crucial practical one for applications. In this paper, we work from a general formulation of hierarchical Bayesian mixed-membership models in Erosheva [15] and Erosheva, Fienberg, and Lafferty [19] and present several model specifications and variations, both parametric and nonparametric, in the context of the learning the number of latent groups and associated patterns for clustering units. Model choice is an issue within specifications, and becomes a component of the larger issue of model comparison. We elucidate strategies for comparing models and specifications by producing novel analyses of two data sets: (1) a corpus of scientific publications from the Proceedings of the National Academy of Sciences (PNAS) examined earlier by Erosheva, Fienberg, and Lafferty [19] and Griffiths and Steyvers [22]; (2) data on functionally disabled American seniors from the National

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.

We consider the statistical analysis of a collection of unipartite graphs, i.e., multiple matrices of relations among objects of a single type. Such data arise, for example, in biological settings, collections of author-recipient email, and social networks. In many applications, clustering the objects of study or situating them in a low dimensional space (e.g., a simplex) is only one of the goals of the analysis. Begin able to estimate relational structures among the clusters themselves is often times as important. For example, in biological applications we are interested in estimating how stable protein complexes (i.e., clusters of proteins) interact. To support such integrated data analyses, we develop the family of “stochastic block models of mixed membership”. Our models combine features of mixed-membership models (Erosheva & Fienberg, 2005) and block models for relational data (Holland et al., 1983) in a hierarchical Bayesian framework. We develop a novel “nested ” variational inference scheme, which is necessary to successfully perform fast approximate posterior inference in our models of relational data. We present evidence to support our claims, using both synthetic data and biological case study. 1.

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This thesis deals with the problem of constructing social networks with topic modeling. To be more specific, it describes how we identify the local communities where people share same interests as well as link this groups together to construct social networks. These problems will be addressed in the course of discussion, and corresponding practical solutions will be provided. I will present the system which fully implements the ideas I propose, in order to achieve the goal. i Acknowledgements I would like to offer my sincerest gratitude to my supervisor, Michael Fourman for his continuous support and encouragement throughout this project. He spent hours discussing with me about the project for both theoretical and practical issues, and ever refused to devote this precious time and intelligence to answering kinds of questions. A special thanks goes to my friend Theodosia Togia, who guide me through my first steps in writing the dissertation and alway there when I need someone to talk to. Many thanks to my friends Cheng Cheng and Ran Cheng for the encouragement they offered to me. I also want to express my thanks to my girlfriend who always comforted me

In a dynamic social or biological environment, the interactions between the underlying actors can undergo large and systematic changes. The latent roles or membership of the actors as determined by these dynamic links will also exhibit rich temporal phenomena, assuming a distinct role at one point while leaning more towards a second role at an another point. To capture this dynamic mixed membership in rewiring networks, we propose a state space mixed membership stochastic blockmodel which embeds an actor into a latent space and track its mixed membership in the latent space across time. We derived efficient approximate learning and inference algorithms for our model, and applied the learned models to analyze a social network between monks, and a rewiring gene interaction network of Drosophila melanogaster collected during its full life cycle. In both cases, our model reveals interesting patterns of the dynamic roles of the actors. 1. Introduction. Inference of network tomography