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.

Network models are widely used to represent relational information among interacting units. In studies of social networks, recent emphasis has been placed on random graph models where the nodes usually represent individual social actors and the edges represent the presence of a specified relation between actors. We develop a class of models where the probability of a relation between actors depends on the positions of individuals in an unobserved "social space." Inference for the social space is developed within a maximum likelihood and Bayesian framework, and Markov chain Monte Carlo procedures are proposed for making inference on latent positions and the effects of observed covariates. We present analyses of three standard datasets from the social networks literature, and compare the method to an alternative stochastic blockmodeling approach. In addition to improving upon model fit, our method provides a visual and interpretable model-based spatial representation of social relationships, and improves upon existing methods by allowing the statistical uncertainty in the social space to be quantified and graphically represented.

Previous work in social network analysis (SNA) has modeled the existence of links from one entity to another, but not the language content or topics on those links. We present the Author-Recipient-Topic (ART) model for social network analysis, which learns topic distributions based on the direction-sensitive messages sent between entities. The model builds on Latent Dirichlet Allocation (LDA) and the Author-Topic (AT) model, adding the key attribute that distribution over topics is conditioned distinctly on both the sender and recipient—steering the discovery of topics according to the relationships between people. We give results on both the Enron email corpus and a researcher’s email archive, providing evidence not only that clearly relevant topics are discovered, but that the ART model better predicts people’s roles. 1 Introduction and Related Work Social network analysis (SNA) is the study of mathematical models for interactions among people, organizations and groups. With the recent availability of large datasets of human

Publication repositories contain an abundance of information about the evolution of scientific research areas. We address the problem of creating a visualization of a research area that describes the flow of topics between papers, quantifies the impact that papers have on each other, and helps to identify key contributions. To this end, we devise a probabilistic topic model that explains the generation of documents; the model incorporates the aspects of topical innovation and topical inheritance via citations. We evaluate the model’s ability to predict the strength of influence of citations against manually rated citations. 1.

Abstract. The presence of autocorrelation provides strong motivation for using relational techniques for learning and inference. Autocorrelation is a statistical dependency between the values of the same variable on related entities and is a nearly ubiquitous characteristic of relational data sets. Recent research has explored the use of collective inference techniques to exploit this phenomenon. These techniques achieve significant performance gains by modeling observed correlations among class labels of related instances, but the models fail to capture a frequent cause of autocorrelation—the presence of underlying groups that influence the attributes on a set of entities. We propose a latent group model (LGM) for relational data, which discovers and exploits the hidden structures responsible for the observed autocorrelation among class labels. Modeling the latent group structure improves model performance, increases inference efficiency, and enhances our understanding of the datasets. We evaluate performance on three relational classification tasks and show that LGM outperforms models that ignore latent group structure when there is little known information with which to seed inference.

discussions. This paper presents recent advances in the statistical modeling of random graphs that have an impact on the empirical study of social networks. Statistical exponential family models (Wasserman and Pattison 1996) are a generalization of the Markov random graph models introduced by Frank and Strauss (1986), which in turn are derived from developments in spatial statistics (Besag 1974). These models recognize the complex dependencies within relational data structures. A major barrier to the application of random graph models to social networks has been the lack of a sound statistical theory to evaluate model fit. This problem has at least three aspects: the specification of realistic models, the algorithmic difficulties of the inferential methods, and the assessment of the degree to which the graph structure produced by the models matches that of the data. We discuss these and related issues of the model degeneracy and inferential degeneracy for commonly used estimators.

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Many datasets of interest today are best described as a linked collection of interrelated objects. These may represent homogeneous networks, in which there is a single-object type and link type, or richer, heterogeneous networks, in which there may be multiple object and link types (and possibly other semantic information). Examples of homogeneous networks include single mode social networks, such as people connected by friendship links, or the WWW, a collection of linked web pages. Examples of heterogeneous networks include those in medical domains describing patients, diseases, treatments and contacts, or in bibliographic domains describing publications, authors, and venues. Link mining refers to data mining techniques that explicitly consider these links when building predictive or descriptive models of the linked data. Commonly addressed link mining tasks include object ranking, group detection, collective classification, link prediction and subgraph discovery. While network analysis has been studied in depth in particular areas such as social network analysis, hypertext mining, and web analysis, only recently has there been a cross-fertilization of ideas among these different communities. This is an exciting, rapidly expanding area. In this article, we review some of the common emerging themes. 1.

As the availability and importance of relational data—such as the friendships summarized on a social networking website—increases, it becomes increasingly important to have good models for such data. The kinds of latent structure that have been considered for use in predicting links in such networks have been relatively limited. In particular, the machine learning community has focused on latent class models, adapting Bayesian nonparametric methods to jointly infer how many latent classes there are while learning which entities belong to each class. We pursue a similar approach with a richer kind of latent variable—latent features—using a Bayesian nonparametric approach to simultaneously infer the number of features at the same time we learn which entities have each feature. Our model combines these inferred features with known covariates in order to perform link prediction. We demonstrate that the greater expressiveness of this approach allows us to improve performance on three datasets. 1

We present a framework for learning abstract relational knowledge with the aim of explaining how people acquire intuitive theories of physical, biological, or social systems. Our approach is based on a generative relational model with latent classes, and simultaneously determines the kinds of entities that exist in a domain, the number of these latent classes, and the relations between classes that are possible or likely. This model goes beyond previous psychological models of category learning, which consider attributes associated with individual categories but not relationships between categories. We apply this domain-general framework to two specific problems: learning the structure of kinship systems and learning causal theories. 1 1