Uncovering latent structure in valued graphs: A variational approach

Mariadassou, Mahendra; Robin, Stéphane; Vacher, Corinne

doi:10.1214/10-aoas361

Cited by 177 publications

(249 citation statements)

References 41 publications

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“…This type of statistical modeling of trophic (feeding) relations is not to be confused with that in ref. 10, which uses compartment membership to explain between-node similarity, nor with that in ref. 11, which employs Bayesian melding (12) to model intercompartmental energy-matter flows subject to mass balance.…”

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confidence: 99%

A unifying approach for food webs, phylogeny, social networks, and statistics

Chiu

Westveld²

2011

Proc. Natl. Acad. Sci. U.S.A.

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A food web consists of nodes, each consisting of one or more species. The role of each node as predator or prey determines the trophic relations that weave the web. Much effort in trophic food web research is given to understand the connectivity structure, or the nature and degree of dependence among nodes. Social network analysis (SNA) techniques—quantitative methods commonly used in the social sciences to understand network relational structure—have been used for this purpose, although postanalysis effort or biological theory is still required to determine what natural factors contribute to the feeding behavior. Thus, a conventional SNA alone provides limited insight into trophic structure. Here we show that by using novel statistical modeling methodologies to express network links as the random response of within- and internode characteristics (predictors), we gain a much deeper understanding of food web structure and its contributing factors through a unified statistical SNA. We do so for eight empirical food webs: Phylogeny is shown to have nontrivial influence on trophic relations in many webs, and for each web trophic clustering based on feeding activity and on feeding preference can differ substantially. These and other conclusions about network features are purely empirical, based entirely on observed network attributes while accounting for biological information built directly into the model. Thus, statistical SNA techniques, through statistical inference for feeding activity and preference, provide an alternative perspective of trophic clustering to yield comprehensive insight into food web structure.

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confidence: 99%

A unifying approach for food webs, phylogeny, social networks, and statistics

Chiu

Westveld²

2011

Proc. Natl. Acad. Sci. U.S.A.

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“…This concept was adapted to stochastic settings and gave rise to the stochastic blockmodel in work by Holland et al (1983) and Fienberg et al (1985). The model 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 2 D. S. CHOI, P. J. WOLFE AND E. M. AIROLDI and extensions thereof have since been applied in a variety of disciplines (Wang & Wong, 1987;Nowicki & Snijders, 2001;Girvan & Newman, 2002;Airoldi et al, 2005;Doreian et al, 2005;Newman, 2006;Handcock et al, 2007;Hoff, 2008;Airoldi et al, 2008;Copic et al, 2009;Mariadassou et al, 2010;Karrer & Newman, 2011). In this work we provide a finite-sample confidence bound that can be used when estimating network structure from data modeled by independent Bernoulli random variates, and also show that under maximum likelihood fitting of a correctly specified K-class blockmodel, the fraction of misclassified network nodes converges in probability to zero even when the number of classes K grows with N .…”

Section: Introductionmentioning

confidence: 99%

Stochastic Blockmodels with Growing Number of Classes

Choi¹,

Wolfe²,

Airoldi³

2011

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND SUBTITLE 13. SUPPLEMENTARY NOTES The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an official Department of the Army position, policy or decision, unless so designated by other documentation. DISTRIBUTION AVAILIBILITY STATEMENTApproved for public release; distribution is unlimited. UU SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)6 Stochastic blockmodels with growing number of classes Report Title ABSTRACTWe present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising a collection of Facebook profiles, resulting in block estimates that reveal residual structure. airoldi@fas.harvard.edu SUMMARY We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least polylogarithmically in this size. We also establish finite-sample confidence bounds on maximumlikelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stocha...

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“…Airoldi et al (2008) develop an alternative latent variable model for social network data where a soft clustering of network actors is achieved; this has been further extended by Xing et al (2010) to model dynamic networks. More recently, Mariadassou et al (2010) and Latouche et al (2010) developed novel latent variable models for finding clusters of actors (or nodes) in network data.…”

Section: Social and Organizational Structurementioning

confidence: 99%