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.

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Abstract—Increasingly, methods to identify community structure in networks have been proposed which allow groups to overlap. These methods have taken a variety of forms, resulting in a lack of consensus as to what characteristics overlapping communities should have. Furthermore, overlapping community detection algorithms have been justified using intuitive arguments, rather than quantitative observations. This lack of consensus and empirical justification has limited the adoption of methods which identify overlapping communities. In this text, we distil from previous literature a minimal set of axioms which overlapping communities should satisfy. Additionally, we modify a previously published algorithm, Iterative Scan, to ensure that these properties are met. By analyzing the community structure of a large blog network, we present both structural and attribute based verification that overlapping communities naturally and frequently occur. Keywords-social network analysis, community detection, overlapping groups I.

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 develop an algorithmic framework for studying the evolution of communities in social networks. We begin with the theoretical foundation, from which we conclude that an evolution is at most as strong as its weakest link. This allows us to formulate an efficient algorithm to identify all evolutionary sequences in a dynamic social network. We use this algorithm to empirically study community evolution in several large social networks, to identify those features of the early stages of a community that indicate whether a community is going to be shortlived or not. Our results show that it is possible to correlate the lifespan of a community to structural parameters of its early evolution; these conclusions are robust across all the social networks we have investigated.

Social processes can be strongly influenced by their spatial and temporal environment, as well as relational structures specific to the process itself. While it has traditionally been expedient to study one or two of these dimensions at a time, it is increasingly feasible to collect data necessary to investigate how, and in what combinations and proportions spatial, temporal and relational (STR) factors govern a process. This proposal is concerned with enabling the early stages of such an analysis, in which the researcher has a hypothesis regarding what relationships exist between STR variables, but not the details and relative strengths of these relationships. Can we express this generalized hypothesis, and algorithmically use available data to recommend a more specific one? I adopt probabilistic graphical models (PGMs) as a flexible framework for representing structural hypotheses, and introduce a templating system for generating regular PGM structures appropriate STR data. In fitting these models to data, I argue against both supervised training and Bayesian unsupervised methods, suggesting a focus on fast, useful inference over (even approximate) optimality. To this end, I introduce Expectation Maximizing belief propagation (EMBP) algorithms, which perform fast unsupervised learning in graphical models with spatial, temporal and relational structure, leading to a variety of

The categorization of vertices in a network is a common task across a multitude of domains. Specifically, structural divisions into internally well connected sets have been shown to be useful in computer science, social science, and biology. In each of these areas, grouping vertices using structural boundaries helps one to understand