Community detection has been an active research area for decades. Among all probabilistic models, Stochastic Block Model has been the most popular one. This paper introduces a novel probabilistic model: RW-HDP, based on random walks and Hierarchical Dirichlet Process, for community extraction. In RW-HDP, random walks conducted in a social network are treated as documents; nodes are treated as words. By using Hierarchical Dirichlet Process, a nonparametric Bayesian model, we are not only able to cluster nodes into different communities, but also determine the number of communities automatically. We use Stochastic Variational Inference for our model inference, which makes our method time efficient and can be easily extended to an online learning algorithm.
@cite_30: We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can easily handle data sets of this size and outperforms traditional variational inference, which can only handle a smaller subset. (We also show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to massive data sets.
@cite_11: Many networks of scientific interest naturally decompose into clusters or communities with comparatively fewer external than internal links; however, current Bayesian models of network communities do not exert this intuitive notion of communities. We formulate a nonparametric Bayesian model for community detection consistent with an intuitive definition of communities and present a Markov chain Monte Carlo procedure for inferring the community structure. A Matlab toolbox with the proposed inference procedure is available for download. On synthetic and real networks, our model detects communities consistent with ground truth, and on real networks, it outperforms existing approaches in predicting missing links. This suggests that community structure is an important structural property of networks that should be explicitly modeled.
@cite_14: 
@cite_7: Modeling structure in complex networks using Bayesian nonparametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This article provides a gentle introduction to nonparametric Bayesian modeling of complex networks: Using an infinite mixture model as running example, we go through the steps of deriving the model as an infinite limit of a finite parametric model, inferring the model parameters by Markov chain Monte Carlo, and checking the model?s fit and predictive performance. We explain how advanced nonparametric models for complex networks can be derived and point out relevant literature.
@cite_15: This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, the sigmoid belief network, the Boltzmann machine, and several variants of hidden Markov models, in which it is infeasible to run exact inference algorithms. We then introduce variational methods, which exploit laws of large numbers to transform the original graphical model into a simplified graphical model in which inference is efficient. Inference in the simpified model provides bounds on probabilities of interest in the original model. We describe a general framework for generating variational transformations based on convex duality. Finally we return to the examples and demonstrate how variational algorithms can be formulated in each case.
@cite_6: 
@cite_19: We propose a series of Bayesian nonparametric statistical models for community detection in graphs. We model the probability of the presence or absence of edges within the graph. Using these models, we naturally incorporate uncertainty and variability and take advantage of nonparametric techniques, such as the Chinese restaurant process and the Dirichlet process. Some of the contributions include: (a) the community structure is directly modeled without specifying the number of communities a priori; (b) the probabilities of edges within or between communities may be modeled as varying by community or pairs of communities; (c) some nodes can be classified as not belonging to any community; and (d) Bayesian model diagnostics are used to compare models and help with appropriate model selection. We start by fitting an initial model to a well-known network dataset, and we develop a series of increasingly complex models. We propose Markov chain Monte Carlo algorithms to carry out the estimation as well as an app...
@cite_5: We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior for the number of mixture components within each group. Given our desire to tie the mixture models in the various groups, we consider a hierarchical model, specifically one in which the base measure for the child Dirichlet processes is itself distributed according to a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessarily share atoms. Thus, as desired, the mixture models in the different groups necessarily share mixture components. We discuss representations of hierarchical Dirichlet processes ...
@cite_31: 
@cite_25: We describe a hierarchical probabilistic model for the detection and recognition of objects in cluttered, natural scenes. The model is based on a set of parts which describe the expected appearance and position, in an object centered coordinate frame, of features detected by a low-level interest operator. Each object category then has its own distribution over these parts, which are shared between objects. We learn the parameters of this model via a Gibbs sampler which uses the graphical model's structure to analytically average over many parameters. Applied to a database of images of isolated objects, the sharing of parts among objects improves detection accuracy when few training examples are available. We also extend this hierarchical framework to scenes containing multiple objects
@cite_17: A key problem in statistical modeling is model selection, that is, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number of clustersinmixturemodelsorthenumberoffactorsinfactoranalysis.Inthistutorial,wedescribeBayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.
Nonparametric Bayesian models are becoming popular these days due to their flexibility @cite_17 , @cite_31 and new posterior inference methods such as Variational Inference @cite_15 , @cite_6 . Teh, Jordan, Beal, and Blei @cite_5 extended the Dirichlet Process to the Hierarchical Dirichlet Process which can also be viewed as an extension of LDA model. Hoffman, Blei, Wang, and Paisley @cite_30 developed the Stochastic Variational Inference for several non-parametric Bayesian models including HDP. In social network research, Morup and Schmidt @cite_11 , @cite_7 formulated a non-parametric Bayesian community generative model for social network analysis. Kim, Gopalan, Blei, and Sudderth @cite_25 proposed the hierarchical Dirichlet process relational model which allowed nodes to have mixed membership in an unbounded set of communities. Guo and Nordman @cite_19 introduced a series of Bayesian nonparametric statistical models for community detection. Blundell and Teh @cite_14 proposed an efficient Bayesian nonparametric model for discovering hierarchical community structure in social networks.