Empirical Bayes estimation for the stochastic blockmodel

Suwan, Shakira; Lee, Dominic S.; Tang, Ronghua; Sussman, Daniel L.; Tang, Minh; Priebe, Carey E.

doi:10.1214/16-ejs1115

Cited by 18 publications

(18 citation statements)

References 27 publications

(40 reference statements)

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“…Proposition 1 shows that as R increases, the approximation in (7) converges to the vanishing-noise approximation given in (4). Proposition 1 also shows that if either d or n − d increase with n, then the covariance does not depend on X i , and is given by R 2 .…”

Section: Gaussian Approximation Of Eigenvectorsmentioning

confidence: 85%

“…One of the most common tasks in network analysis is the search for community structure among units in the network. Much of the statistical [5][6][7] and information theoretical [8][9][10][11] work on community detection studies the stochastic block model (SBM) [12]. In this probabilistic network model, the probability of an edge between individuals i and j is governed exclusively by their community memberships, X i , and X j .…”

Section: Introductionmentioning

confidence: 99%

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Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise

Mathews

Mayya

Volfovsky

et al. 2019

2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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Community detection tasks have received a lot of attention across statistics, machine learning, and information theory with a large body of work concentrating on theoretical guarantees for the stochastic block model. One line of recent work has focused on modeling the spectral embedding of a network using Gaussian mixture models (GMMs) in scaling regimes where the ability to detect community memberships improves with the size of the network. However, these regimes are not very realistic. This paper provides tractable methodology motivated by new theoretical results for networks with non-vanishing noise. We present a procedure for community detection using GMMs that incorporates certain truncation and shrinkage effects that arise in the non-vanishing noise regime. We provide empirical validation of this new representation using both simulated and real-world data.

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Section: Gaussian Approximation Of Eigenvectorsmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise

Mathews

Mayya

Volfovsky

et al. 2019

2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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“…We apply this spectral clustering approaches to two Wikipedia graphs [59]. The vertices of these graphs represent Wikipedia article pages.…”

Section: Real Data Experiments 3: Joint Embedding To Cluster Verticesmentioning

confidence: 99%

Joint Embedding of Graphs

Wang

Arroyo

Vogelstein

et al. 2021

IEEE Trans. Pattern Anal. Mach. Intell.

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Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.

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“…To begin, we consider graphs representing a subset of Wikipedia (Suwan et al, 2016). The data set is accessible at http://www.cis.jhu.edu/~parky/Data/data.html.…”

Section: Wikipedia Datamentioning

confidence: 99%

The Multiple Random Dot Product Graph Model

Nielsen,

Witten

2018

Preprint

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Data in the form of graphs, or networks, arise naturally in a number of contexts; examples include social networks and biological networks. We are often faced with the availability of multiple graphs on a single set of nodes. In this article, we propose the multiple random dot product graph model for this setting. Our proposed model leads naturally to an optimization problem, which we solve using an efficient alternating minimization approach. We further use this model as the basis for a new test for the hypothesis that the graphs come from a single distribution, versus the alternative that they are drawn from different distributions. We evaluate the performance of both the fitting algorithm and the hypothesis test in several simulation settings, and demonstrate empirical improvement over existing approaches. We apply these new approaches to a Wikipedia data set and a C. elegans data set.

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Empirical Bayes estimation for the stochastic blockmodel

Cited by 18 publications

References 27 publications

Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise

Gaussian Mixture Models for Stochastic Block Models with Non-Vanishing Noise

Joint Embedding of Graphs

The Multiple Random Dot Product Graph Model

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