A local structure model for network analysis

Casleton, Emily; Nordman, Daniel; Kaiser, Mark

doi:10.4310/SII.2017.v10.n2.a15

Title: A local structure model for network analysis

Abstract

The statistical analysis of networks is a popular research topic with ever widening applications. Exponential random graph models (ERGMs), which specify a model through interpretable, global network features, are common for this purpose. In this study we introduce a new class of models for network analysis, called local structure graph models (LSGMs). In contrast to an ERGM, a LSGM specifies a network model through local features and allows for an interpretable and controllable local dependence structure. In particular, LSGMs are formulated by a set of full conditional distributions for each network edge, e.g., the probability of edge presence/absence, depending on neighborhoods of other edges. Additional model features are introduced to aid in specification and to help alleviate a common issue (occurring also with ERGMs) of model degeneracy. Finally, the proposed models are demonstrated on a network of tornadoes in Arkansas where a LSGM is shown to perform significantly better than a model without local dependence.

Authors:

Casleton, Emily ^[1]; Nordman, Daniel ^[2]; Kaiser, Mark ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Iowa State Univ., Ames, IA (United States). Dept. of Statistics

Publication Date:: Sat Apr 01 00:00:00 EDT 2017

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE; SNL Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)

OSTI Identifier:: 1409754

Report Number(s):: LA-UR-16-20622
Journal ID: ISSN 1938-7989

Grant/Contract Number:: AC52-06NA25396; DMS-1406747

Resource Type:: Accepted Manuscript

Journal Name:: Statistics and Its Interface

Additional Journal Information:: Journal Volume: 10; Journal Issue: 2; Journal ID: ISSN 1938-7989

Publisher:: International Press of Boston, Inc.

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Mathematics

Citation Formats


                    Casleton, Emily, Nordman, Daniel, and Kaiser, Mark. A local structure model for network analysis.  United States: N. p., 2017. 
Web.  doi:10.4310/SII.2017.v10.n2.a15.

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                    Casleton, Emily, Nordman, Daniel, & Kaiser, Mark. A local structure model for network analysis.  United States.  https://doi.org/10.4310/SII.2017.v10.n2.a15

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                    Casleton, Emily, Nordman, Daniel, and Kaiser, Mark. Sat .  
"A local structure model for network analysis".  United States.  https://doi.org/10.4310/SII.2017.v10.n2.a15.  https://www.osti.gov/servlets/purl/1409754.

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@article{osti_1409754,

  title        = {A local structure model for network analysis},

  author       = {Casleton, Emily and Nordman, Daniel and Kaiser, Mark},

  abstractNote = {The statistical analysis of networks is a popular research topic with ever widening applications. Exponential random graph models (ERGMs), which specify a model through interpretable, global network features, are common for this purpose. In this study we introduce a new class of models for network analysis, called local structure graph models (LSGMs). In contrast to an ERGM, a LSGM specifies a network model through local features and allows for an interpretable and controllable local dependence structure. In particular, LSGMs are formulated by a set of full conditional distributions for each network edge, e.g., the probability of edge presence/absence, depending on neighborhoods of other edges. Additional model features are introduced to aid in specification and to help alleviate a common issue (occurring also with ERGMs) of model degeneracy. Finally, the proposed models are demonstrated on a network of tornadoes in Arkansas where a LSGM is shown to perform significantly better than a model without local dependence.},

  doi          = {10.4310/SII.2017.v10.n2.a15},

  journal      = {Statistics and Its Interface},

  number       = 2,

  volume       = 10,

  place        = {United States},

  year         = {Sat Apr 01 00:00:00 EDT 2017},

  month        = {Sat Apr 01 00:00:00 EDT 2017}

}

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Journal Article:

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https://doi.org/10.4310/SII.2017.v10.n2.a15

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Cited by: 6 works

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Figures / Tables:

Figure 1: Two example networks and dependence structures with resulting dependence graphs. The nodes of the dependence graph corresponds to the edges of the original graph. An edge in the dependence graph indicates conditional dependence between two random variables (i.e., two edges) in the original graph.

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Works referencing / citing this record:

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler
journal, October 2019

Kaplan, Andee; Kaiser, Mark S.; Lahiri, Soumendra N.
Journal of Computational and Graphical Statistics, Vol. 29, Issue 2
DOI: 10.1080/10618600.2019.1668800

Simulating Markov random fields with a conclique-based Gibbs sampler
text, January 2018

Kaplan, Andee; Kaiser, Mark S.; Lahiri, Soumendra N.
arXiv
DOI: 10.48550/arxiv.1808.04739

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Title: A local structure model for network analysis

Abstract

Citation Formats

Figures / Tables:

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler journal, October 2019

Simulating Markov random fields with a conclique-based Gibbs sampler text, January 2018

Simulating Markov Random Fields With a Conclique-Based Gibbs Sampler
journal, October 2019

Simulating Markov random fields with a conclique-based Gibbs sampler
text, January 2018