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.

Characterizing the relationship that exists between a person’s social group and his/her personal behavior has been a long standing goal of social network analysts. In this paper, we apply data mining techniques to study this relationship for a population of over 10 million people, by turning to online sources of data. The analysis reveals that people who chat with each other (using instant messaging) are more likely to share interests (their Web searches are the same or topically similar). The more time they spend talking, the stronger this relationship is. People who chat with each other are also more likely to share other personal characteristics, such as their age and location (and, they are likely to be of opposite gender). Similar findings hold for people who do not necessarily talk to each other but do have a friend in common. Our analysis is based on a well-defined mathematical formulation of the problem, and is the largest such study we are aware of. Categories and Subject Descriptors

A multi-mode network typically consists of multiple heterogeneous social actors among which various types of interactions could occur. Identifying communities in a multi-mode network can help understand the structural properties of the network, address the data shortage and unbalanced problems, and assist tasks like targeted marketing and finding influential actors within or between groups. In general, a network and the membership of groups often evolve gradually. In a dynamic multi-mode network, both actor membership and interactions can evolve, which poses a challenging problem of identifying community evolution. In this work, we try to address this issue by employing the temporal information to analyze a multi-mode network. A spectral framework and its scalability issue are carefully studied. Experiments on both synthetic data and real-world large scale networks demonstrate the efficacy of our algorithm and suggest its generality in solving problems with complex relationships.

Abstract: We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including maximum likelihood estimation algorithms. We discuss models of this type and their properties, and give examples, as well as a demonstration of their use for hypothesis testing and classification. We believe our temporal ERG models represent a useful new framework for modeling time-evolving social networks, and rewiring networks from other domains such as gene regulation circuitry, and communication networks. Received November 2009. 1.

Social media such as blogs, Facebook, Flickr, etc., presents data in a network format rather than classical IID distribution. To address the interdependency among data instances, relational learning has been proposed, and collective inference based on network connectivity is adopted for prediction. However, the connections in social media are often multi-dimensional. An actor can connect to another actor due to different factors, e.g., alumni, colleagues, living in the same city or sharing similar interest, etc. Collective inference normally does not differentiate these connections. In this work, we propose to extract latent social dimensions based on network information first, and then utilize them as features for discriminative learning. These social dimensions describe different affiliations of social actors hidden in the network, and the subsequent discriminative learning can automatically determine which affiliations are better aligned with the class labels. Such a scheme is preferred when multiple diverse relations are associated with the same network. We conduct extensive experiments on social media data (one from a real-world blog site and the other from a popular content sharing site). Our model outperforms representative relational learning methods based on collective inference, especially when few labeled data are available. The sensitivity of this model and its connection to existing methods are also carefully examined.

Economic Forum within the framework of the

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.

Proportional representation by means of a single transferable vote (PR-STV) 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 D-dimensional space. The locations are determined by the ranked preferences which are modeled using the Plackett-Luce model for rank data. Voter positions reflect their preferences while the candidate locations represent the global view of the candidates by the electorate. 1.

This paper addresses the problem of unsupervised group discovery in social networks. We adopt a nonparametric Bayesian framework that extends previous models to networks where the interacting objects can simultaneously belong to several groups (i.e., mixed membership). For this purpose, a hierarchical nonparametric prior is utilized and inference is performed using Gibbs sampling. The resulting mixed-membership model combines the usual advantages of nonparametric models, such as inference of the total number of groups from the data, and provides a more flexible modeling environment by quantifying the degrees of membership to the various groups. Such models are useful for social information processing because they can capture a user’s multiple interests and hobbies.

Presence-absence (0-1) observations are special in that often the absence of evidence is not evidence of absence. Here we develop an independent factor model, which has the unique capability to isolate the former as an independent discrete binary noise factor. This representation then forms the basis of inferring missed presences by means of denoising. This is achieved in a probabilistic formalism, employing independent Beta latent source densities and a Bernoulli data likelihood model. Variational approximations are employed to make the inferences tractable. We relate our model to existing models of 0-1 data, demonstrating its advantages for the problem considered, and we present applications in several problem domains, including social network analysis and DNA fingerprint analysis. Key words: factor models, data denoising, 0-1 data 1