Bayesian estimation of the latent dimension and communities in stochastic blockmodels

Passino, Francesco Sanna; Heard, Nicholas A.

doi:10.1007/s11222-020-09946-6

Cited by 14 publications

(6 citation statements)

References 58 publications

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“…An important future work is the estimation of K for directed networks. Various techniques have been proposed to estimate K for undirected network [28,21,7,36,4,30,13,17], how to extend these techniques to determine K for directed network leaves to be studied. [43,8,23] study the problem of community detection under SBM and DCSBM by modularity maximization approaches, and it is of interest to extend these techniques to study directed networks.…”

Section: Discussionmentioning

confidence: 99%

Directed degree corrected mixed membership model and estimating community memberships in directed networks

Qing¹

2021

Preprint

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This paper considers the problem of modeling and estimating community memberships of nodes in a directed network where every row (column) node is associated with a vector determining its membership in each row (column) community. To model such directed network, we propose directed degree corrected mixed membership (DiDCMM) model by considering degree heterogeneity. DiDCMM is identifiable under popular conditions for mixed membership network when considering degree heterogeneity. Based on the cone structure inherent in the normalized version of the left singular vectors and the simplex structure inherent in the right singular vectors of the population adjacency matrix, we build an efficient algorithm called DiMSC to infer the community membership vectors for both row nodes and column nodes. By taking the advantage of DiMSC's equivalence algorithm which returns same estimations as DiMSC and the recent development on row-wise singular vector deviation, we show that the proposed algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vectors of each row node and each column node under DiDCMM. The theory is supplemented by a simulation study.

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Section: Discussionmentioning

confidence: 99%

Directed degree corrected mixed membership model and estimating community memberships in directed networks

Qing¹

2021

Preprint

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“…However, ideally, a “good” community detection algorithm should be not only validated empirically but also demonstrate a reliable theoretical basis. Statistical methods for extracting communities in complex networks aim to address this question by revealing the latent structure of the network based on model fitting and the associated statistical inference (Bickel & Sarkar, 2016; He et al, 2020; Lancichinetti et al, 2011; Saldaña et al, 2017; Sanna Passino & Heard, 2020).…”

Section: Stochastic Block Modelsmentioning

confidence: 99%

Community detection in complex networks: From statistical foundations to data science applications

Dey

Tian

Gel

2021

WIREs Computational Stats

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Identifying and tracking community structures in complex networks are one of the cornerstones of network studies, spanning multiple disciplines, from statistics to machine learning to social sciences, and involving even a broader range of application areas, from biology to politics to blockchain. This survey paper aims to provide an overview of some most popular approaches in statistical network community detection as well as the newly emerging research directions such as community extraction with higher‐order features and community discovery in multilayer and multiscale networks. Our goal is to offer a unified view at methodological interconnections and the wide spectrum of interdisciplinary data science applications of network community analysis. This article is categorized under: Data: Types and Structure > Graph and Network Data Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and Classification

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“…Zhou and Amini (2019) considered spectral clustering algorithms for community detection under a general bipartite SBM by proposing a new data-driven regularization that can restore the concentration of the adjacency matrix even for the sparse networks. Passino and Heard (2020) proposed a novel Bayesian model for simultaneous and automatic selection of the appropriate dimension of the latent classes and the number of blocks and extended to directed and bipartite graphs. Sun (2021) constructed a generative bipartite degree-corrected mixed membership SBM and proposed a variational expectation-maximization (EM) algorithm to fit their model.…”

Section: Introduction 1background: Bipartite Networkmentioning

confidence: 99%

Analysis of Connection Times in Bipartite Network Data: Development of the Bayesian Latent Space Accumulator Model with Applications to Assessment Data

Yun¹,

Kim²,

Jeon³

et al. 2022

Preprint

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Conventional social network analysis typically focuses on analyzing the structure of the connections between pairs of nodes in a sample dataset. However, the process and the consequences of how long it takes pairs of nodes to be connected, i.e., node connection times, on the network structure have been understudied in the literature. In this article, we propose a novel statistical approach, socalled the latent space accumulator model, for modeling connection times and their influence on the structure of connections. We focus on a special type of bipartite network composed of respondents and test items, where connection outcomes are binary and mutually exclusive. To model connection times for each connection outcome, we leverage ideas from the competing risk modeling approach and embed latent spaces into the competing risk models to capture heterogeneous dependence structures of connection times across connection outcome types. The proposed approach is applied and illustrated with two real data examples.

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Bayesian estimation of the latent dimension and communities in stochastic blockmodels

Cited by 14 publications

References 58 publications

Directed degree corrected mixed membership model and estimating community memberships in directed networks

Directed degree corrected mixed membership model and estimating community memberships in directed networks

Community detection in complex networks: From statistical foundations to data science applications

Analysis of Connection Times in Bipartite Network Data: Development of the Bayesian Latent Space Accumulator Model with Applications to Assessment Data

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