Mixed Membership Stochastic Blockmodels

By Edoardo M. Airoldi, David M. Blei, Stephen E. Fienberg, Eric P. Xing. 2007

2,215 citations recorded by the source corpus.

Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data with probabilisic models can be delicate because the simple exchangeability assumptions underlying many boilerplate models no longer hold. In this paper, we describe a latent variable model of such data called the mixed membership stochastic blockmodel. This model extends blockmodels for relational data to ones which capture mixed membership latent relational structure, thus providing an object-specific low-dimensional representation. We develop a general variational inference algorithm for fast approximate posterior inference. We explore applications to social and protein interaction networks.

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, background): “…control and reinforcement learning (Van Den Broek, Wiegerinck, and Kap-pen 2008; Furmston and Barber 2010), statistical network analysis (Wiggins and Hofman 2008; Airoldi et al. 2008), astronomy (Regier et al. 2015), and the social sciences (Erosheva, Fienberg, and Joutard 2007; Grimmer 2011).”
GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models (2018, methodology): “In addition, we compare against popular generative models that include learnable parameters: Kronecker graph models (Leskovec et al., 2010) and mixed-membership stochastic block models (MMSB) (Airoldi et al., 2008).”
Privacy for Free: Posterior Sampling and Stochastic Gradient Monte Carlo (2015, methodology): “social networks (Airoldi et al., 2009), brain activity (Penny et al.”
Probabilistic Latent Document Network Embedding (2014, background): “For instance, in mixed membership stochastic blockmodel [21], each user is associated with a distribution over “communities”, which explain the generation of links among users.”
Generalized Latent Factor Models for Social Network Analysis (2011, methodology): “In this paper, we focus on latent variable models [Bartholomew and Knott, 1999] which have been successfully applied to model social networks [Hoff, 2008; Nowicki and Snijders, 2001; Hoff et al., 2002; Kemp et al., 2006; Airoldi et al., 2008; Hoff, 2009].”
Exact Recovery in the Stochastic Block Model (2014, background): “Finally, it is natural to expect that the results obtained in this paper extend to a much more general family of network models, with multiple clusters, overlapping communities [4] and labelled edges [40].”
Learning to Discover Social Circles in Ego Networks (2012, methodology): “Our model has two innovations: First, in contrast to mixed-membership models [2] we predict hard assignment of a node to multiple circles, which proves critical for good performance.”
Weisfeiler-Lehman Neural Machine for Link Prediction (2017, methodology): “It has many applications, such as friend recommendation in social networks [2], product recommendation in e-commerce [3], knowledge graph completion [4], finding interactions between proteins [5], and recovering missing reactions in metabolic networks [6].”
Efficient discovery of overlapping communities in massive networks (2013, methodology): “This has been a successful approach for probability models of small networks (6, 10).”
Matrix estimation by Universal Singular Value Thresholding (2012, background): “[5, 57]. Note that distance matrices and stochastic blockmodels are both special cases of latent space models. There have been various attempts to estimate parameters in the latent space models (e.g. [55, 53, 4]). Almost all of these approaches rely on heuristic arguments and justication through sim”
A mixture of experts model for rank data with applications in election studies (2008, methodology): “An alternative extension to the mixture model is the mixed membership model for multivariate binary data [Pritchard, Stephens and Peter (2000), Erosheva, Fienberg and Joutard (2007)] and network data [Airoldi et al. (2008)]; such models could be used to study voting blocs in elections that use an ap”
Relational learning via latent social dimensions (2009, methodology): “Community detection has been an active field in social network analysis and various methods have been proposed including stochastic block model [28, 1], latent space model [12, 11], spectral clustering [37], hierarchical clustering based on various measures such as shortest-path betweenness [27] or ”
Homophily and Contagion Are Generically Confounded in Observational Social Network Studies (2010, background): “…of the block structure may make the problem worse — consider the cases where the generating mechanism may be a mixed-membership block model (Airoldi et al., 2008) or “role” model (Reichardt and White, 2007) but communities are “discovered” assuming a simple modular network structure.”
Statistical Inference on Random Dot Product Graphs: a Survey (2017, methodology): “In [3], Airoldi et al define the important generalization of a mixed-membership stochastic blockmodel, in which block membership may change depending on vertex-to-vertex interactions, and the authors demonstrate methods of inference for the mixed membership and block probabilities.”
Build, Compute, Critique, Repeat: Data Analysis with Latent Variable Models (2014, background): “, 2007), and communities in networks (Airoldi et al., 2008)—but that each group exhibits a different subset of those patterns and to different degrees.”
Community-Affiliation Graph Model for Overlapping Network Community Detection (2012, methodology): “We use the Bayes Information Criterion as described in [2] to choose K.”
Block-LDA: Jointly Modeling Entity-Annotated Text and Entity-Entity Links (2014, methodology): “We see that the F1 scores for the baseline sparse block model and MMSB are nearly the same and that combining text and links provides a significant boost to the F1 score.”