Moments of parameter estimates for Chung-Lu random graph models

Nicholas Arcolano, Karl Ni, Benjamin A. Miller, Nadya Bliss, Patrick J. Wolfe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)

Abstract

As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.

Original languageEnglish (US)
Title of host publicationICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Pages3961-3964
Number of pages4
DOIs
StatePublished - 2012
Externally publishedYes
Event2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012 - Kyoto, Japan
Duration: Mar 25 2012Mar 30 2012

Other

Other2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012
CountryJapan
CityKyoto
Period3/25/123/30/12

Fingerprint

Signal processing
Statistical Models

Keywords

  • central limit theory
  • delta method
  • given expected degree models
  • graphs and networks
  • parameter estimation

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

Cite this

Arcolano, N., Ni, K., Miller, B. A., Bliss, N., & Wolfe, P. J. (2012). Moments of parameter estimates for Chung-Lu random graph models. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings (pp. 3961-3964). [6288785] https://doi.org/10.1109/ICASSP.2012.6288785

Moments of parameter estimates for Chung-Lu random graph models. / Arcolano, Nicholas; Ni, Karl; Miller, Benjamin A.; Bliss, Nadya; Wolfe, Patrick J.

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012. p. 3961-3964 6288785.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Arcolano, N, Ni, K, Miller, BA, Bliss, N & Wolfe, PJ 2012, Moments of parameter estimates for Chung-Lu random graph models. in ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings., 6288785, pp. 3961-3964, 2012 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012, Kyoto, Japan, 3/25/12. https://doi.org/10.1109/ICASSP.2012.6288785
Arcolano N, Ni K, Miller BA, Bliss N, Wolfe PJ. Moments of parameter estimates for Chung-Lu random graph models. In ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012. p. 3961-3964. 6288785 https://doi.org/10.1109/ICASSP.2012.6288785
Arcolano, Nicholas ; Ni, Karl ; Miller, Benjamin A. ; Bliss, Nadya ; Wolfe, Patrick J. / Moments of parameter estimates for Chung-Lu random graph models. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2012. pp. 3961-3964
@inproceedings{7c2e79fc3bf34d68ac7b2c3810702a74,
title = "Moments of parameter estimates for Chung-Lu random graph models",
abstract = "As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.",
keywords = "central limit theory, delta method, given expected degree models, graphs and networks, parameter estimation",
author = "Nicholas Arcolano and Karl Ni and Miller, {Benjamin A.} and Nadya Bliss and Wolfe, {Patrick J.}",
year = "2012",
doi = "10.1109/ICASSP.2012.6288785",
language = "English (US)",
isbn = "9781467300469",
pages = "3961--3964",
booktitle = "ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings",

}

TY - GEN

T1 - Moments of parameter estimates for Chung-Lu random graph models

AU - Arcolano, Nicholas

AU - Ni, Karl

AU - Miller, Benjamin A.

AU - Bliss, Nadya

AU - Wolfe, Patrick J.

PY - 2012

Y1 - 2012

N2 - As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.

AB - As abstract representations of relational data, graphs and networks find wide use in a variety of fields, particularly when working in non-Euclidean spaces. Yet for graphs to be truly useful in in the context of signal processing, one ultimately must have access to flexible and tractable statistical models. One model currently in use is the Chung-Lu random graph model, in which edge probabilities are expressed in terms of a given expected degree sequence. An advantage of this model is that its parameters can be obtained via a simple, standard estimator. Although this estimator is used frequently, its statistical properties have not been fully studied. In this paper, we develop a central limit theory for a simplified version of the Chung-Lu parameter estimator. We then derive approximations for moments of the general estimator using the delta method, and confirm the effectiveness of these approximations through empirical examples.

KW - central limit theory

KW - delta method

KW - given expected degree models

KW - graphs and networks

KW - parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=84867593239&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867593239&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2012.6288785

DO - 10.1109/ICASSP.2012.6288785

M3 - Conference contribution

AN - SCOPUS:84867593239

SN - 9781467300469

SP - 3961

EP - 3964

BT - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

ER -