Bayesian community detection

S. L. van der Pas; A. W. van der Vaart

doi:https://doi.org/10.1214/17-BA1078

Bayesian community detection

S. L. van der Pas, A. W. van der Vaart

Research output: Contribution to journal › Article › Academic › peer-review

16 Citations (Scopus)

Abstract

We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities.We show that this estimator is strongly consistent when the expected degree is at least of order log² n, where n is the number of nodes in the network.

Original language	English
Pages (from-to)	767-796
Number of pages	30
Journal	Bayesian Analysis
Volume	13
Issue number	3
DOIs	https://doi.org/10.1214/17-BA1078
Publication status	Published - 1 Sept 2018
Externally published	Yes

Keywords

Bayesian inference
Community detection
Consistency
MAP estimation
Modularities
Networks
Stochastic block model

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title = "Bayesian community detection",

abstract = "We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities.We show that this estimator is strongly consistent when the expected degree is at least of order log2 n, where n is the number of nodes in the network.",

keywords = "Bayesian inference, Community detection, Consistency, MAP estimation, Modularities, Networks, Stochastic block model",

author = "{van der Pas}, {S. L.} and {van der Vaart}, {A. W.}",

note = "Funding Information: ∗Research supported by Netherlands Organization for Scientific Research NWO. †The research leading to these results has received funding from the European Research under ERC Grant Agreement 320637. ‡Mathematical Institute, Leiden University, svdpas@math.leidenuniv.nl §Mathematical Institute, Leiden University, avdvaart@math.leidenuniv.nl Publisher Copyright: {\textcopyright} 2018 International Society for Bayesian Analysis. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

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doi = "https://doi.org/10.1214/17-BA1078",

language = "English",

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AU - van der Pas, S. L.

AU - van der Vaart, A. W.

N1 - Funding Information: ∗Research supported by Netherlands Organization for Scientific Research NWO. †The research leading to these results has received funding from the European Research under ERC Grant Agreement 320637. ‡Mathematical Institute, Leiden University, svdpas@math.leidenuniv.nl §Mathematical Institute, Leiden University, avdvaart@math.leidenuniv.nl Publisher Copyright: © 2018 International Society for Bayesian Analysis. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities.We show that this estimator is strongly consistent when the expected degree is at least of order log2 n, where n is the number of nodes in the network.

AB - We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode corresponding to a Dirichlet prior on the class proportions, a generalized Bernoulli prior on the class labels, and a beta prior on the edge probabilities.We show that this estimator is strongly consistent when the expected degree is at least of order log2 n, where n is the number of nodes in the network.

KW - Bayesian inference

KW - Community detection

KW - Consistency

KW - MAP estimation

KW - Modularities

KW - Networks

KW - Stochastic block model

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U2 - https://doi.org/10.1214/17-BA1078

DO - https://doi.org/10.1214/17-BA1078

M3 - Article

SN - 1936-0975

VL - 13

SP - 767

EP - 796

JO - Bayesian Analysis

JF - Bayesian Analysis

IS - 3

ER -

Bayesian community detection

Abstract

Keywords

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