Bayesian approach to network modularity.

By Jake M. Hofman, Chris H. Wiggins. 2007

318 citations recorded by the source corpus.

We present an efficient, principled, and interpretable technique for inferring module assignments and for identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how the method overcomes the resolution limit problem, accurately recovering the true number of modules. Our approach is based on Bayesian methods for model selection which have been used with success for almost a century, implemented using a variational technique developed only in the past decade. We apply the technique to synthetic and real networks and outline how the method naturally allows selection among competing models.

Subfields: Artificial Intelligence, Molecular Biology, Statistical and Nonlinear Physics

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, background): “…optimal 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…”
Community detection in graphs (2009, background): “Hofman and Wiggins have proposed a general Bayesian approach to the problem of graph clustering [304].”
A classification for community discovery methods in complex networks (2011, methodology): “t techniques, but share the same meta deﬁnition of community proposed in this section, are: MetaFac [31], a hypergraph factorization technique; a physical-chemical algorithm using a Bayesian approach [32]; a local density-based approach called LA → IS2 [33]; and another proposed function used to mea”
fastSTRUCTURE: Variational Inference of Population Structure in Large SNP Data Sets (2014, methodology): “Variational methods, originally used for approximating intractable integrals, have been used for a wide variety of applications in complex networks (Hofman and Wiggins 2008), machine learning (Jordan et al. 1998; Blei et al. 2003), and Bayesian variable selection (Logsdon et al. 2010; Carbonetto…”
Infinite multiple membership relational modeling for complex networks (2011, unknown): “In the model proposed by [10] (HW) the class link probability, ρk , is specified by a within-class probability ρc and a betweenclass probability ρ0.”
Communities in Networks (2009, background): “tion to optimize. For example, modularity has a known resolution limit (see Section 3.8) that might cause one to miss important communities [32]. A few alternatives to modularity have been considered [5,33,50,61,109], and it is ultimately desirable to optimize a quality function that includes not on”
Relational Topic Models for Document Networks (2009, background): “Several latent space models for modeling network structure have been proposed (Kemp et al. 2004; Hoff et al. 2002; Hofman and Wiggins 2007; Airoldi et al. 2008); though powerful, these models only account for links in the data and cannot model node attributes as well.”
Finding overlapping communities in networks by label propagation (2009, methodology): “The algorithms use a wide vari ty of techniques, including removal of highbetweenness edges [1], optimization of modularity [2], detection of dense subgraphs [3], statistical inference [4], and many more.”
Hierarchical block structures and high-resolution model selection in large networks (2013, methodology): “…is one of the many principled methods one could use to do model selection, which include, e.g., Bayesian model selection via integrated likelihood [21, 38, 39, 41, 42, 55], likelihood ratios [56] or more approximative methods such as Bayesian information criterion (BIC) [57] and Akaike…”
Learning Latent Block Structure in Weighted Networks (2014, methodology): “Here, we describe an eﬃcient variational Bayes approach [5, 16], which eﬀectively handles one technical diﬃculty in ﬁtting the model to real data.”
Detecting communities and their evolutions in dynamic social networks—a Bayesian approach (2011, methodology): “SBM is a well studied statistical model that has been successfully used in social network analysis (Hofman and Wiggins 2008; Holland and Leinhardt 1976).”
Efficient discovery of overlapping communities in massive networks (2013, methodology): “This has been a successful approach for probability models of small networks (6, 10).”