Variational Bayesian inference and complexity control for stochastic block models

Latouche, Pierre; Birmelé, Étienne; Ambroise, Christophe

doi:10.1177/1471082x1001200105

Cited by 144 publications

(143 citation statements)

References 33 publications

(62 reference statements)

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“…Apart from CL-BIC and BIC, we also consider the Integrated Likelihood Variational Bayes (VB) approach of Latouche et al (2012). To estimate the true community number, their method selects the candidate value k which maximizes a variational Bayes approximation to the observed-data log-likelihood.…”

Section: Simulationsmentioning

confidence: 99%

“…The remaining entries of θ are set to 0.05. Hence, following Latouche et al (2012), vertices from community 4 connect with probability 0.35 to any other vertices in the network, forming a community of only hubs. Community sizes are the same as in Simulation 1, with results collected in Table 3.…”

Section: Simulationsmentioning

confidence: 99%

“…For the literature addressing the problem of selecting K, besides the block-wise edge splitting method of Chen and Lei (2014), a common practice is to use BIC-type criteria (Airoldi et al, 2008;Daudin et al, 2008) or a variational Bayes approach (Latouche et al, 2012;Hunter et al, 2012). An inherently related problem is that of selecting the number of components in mixture models, where the birth-and-death point process of Stephens (2000) and the allocation sampler of Nobile and Fearnside (2007) provide two fully Bayesian approaches in the case where K is finite but unknown.…”

Section: Introductionmentioning

confidence: 99%

“…Using techniques from the composite likelihood paradigm (Lindsay, 1988), we develop a composite likelihood BIC (CL-BIC) approach (Gao and Song, 2010) for selecting the community number in the situation where assumed independencies in the stochastic blockmodel and other exchangeable graph models do not hold. The procedure is tested on simulated and real data, and is shown to outperform two competitors -traditional BIC and the variational Bayes criterion of Latouche et al (2012), in terms of model selection consistency.…”

Section: Introductionmentioning

confidence: 99%

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How Many Communities Are There?

Saldana

Feng

2017

Journal of Computational and Graphical Statistics

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Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online.

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Section: Simulationsmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How Many Communities Are There?

Saldana

Feng

2017

Journal of Computational and Graphical Statistics

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“…Other techniques to extract the number of groups have been proposed (Côme and Latouche, 2015;Daudin et al, 2008;Handcock et al, 2007;Latouche et al, 2012;Newman and Reinert, 2016).…”

Section: E Methods Based On Statistical Inferencementioning

confidence: 99%

Community detection in networks: A user guide

2016

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Community detection in networks is one of the most popular topics of modern network science. Communities, or clusters, are usually groups of vertices having higher probability of being connected to each other than to members of other groups, though other patterns are possible. Identifying communities is an ill-defined problem. There are no universal protocols on the fundamental ingredients, like the definition of community itself, nor on other crucial issues, like the validation of algorithms and the comparison of their performances. This has generated a number of confusions and misconceptions, which undermine the progress in the field. We offer a guided tour through the main aspects of the problem. We also point out strengths and weaknesses of popular methods, and give directions to their use.

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Consistent estimation of the number of communities in stochastic block models using cross‐validation

Qin

Lei

2022

Stat

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The stochastic block model (SBM) and its variants constitute an important family of probabilistic tools for studying network data. There is a rich literature on methods for estimating block labels and model parameters of stochastic block models. Most of these studies require the number of communities K as an input, making the estimation of K an important problem. Cross-validation is a natural option for this problem since it is a widely used generic method for evaluating model fitting. However, crossvalidation is known to be inconsistent and prone to overfitting unless impractical split ratios are used. Cross-validation with confidence (CVC) is proposed with better theoretical guarantees in conventional settings. We study the properties of CVC for stochastic block models. Our theoretical studies show that CVC, unlike the standard cross-validation, can consistently pick the optimal K under suitable conditions. We implement this method and check its performance against other established methods on both synthetic and real datasets.

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Variational Bayesian inference and complexity control for stochastic block models

Cited by 144 publications

References 33 publications

How Many Communities Are There?

How Many Communities Are There?

Community detection in networks: A user guide

Consistent estimation of the number of communities in stochastic block models using cross‐validation

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