Article

Graph model selection using maximum likelihood

Authors:

Ivona Bezáková,

Rahul SanthanamAuthors Info & Claims

ICML '06: Proceedings of the 23rd international conference on Machine learning

Pages 105 - 112

https://doi.org/10.1145/1143844.1143858

Published: 25 June 2006 Publication History

Abstract

In recent years, there has been a proliferation of theoretical graph models, e.g., preferential attachment and small-world models, motivated by real-world graphs such as the Internet topology. To address the natural question of which model is best for a particular data set, we propose a model selection criterion for graph models. Since each model is in fact a probability distribution over graphs, we suggest using Maximum Likelihood to compare graph models and select their parameters. Interestingly, for the case of graph models, computing likelihoods is a difficult algorithmic task. However, we design and implement MCMC algorithms for computing the maximum likelihood for four popular models: a power-law random graph model, a preferential attachment model, a small-world model, and a uniform random graph model. We hope that this novel use of ML will objectify comparisons between graph models.

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Cited By

Johnson SHenderson DBoys R(2022)On Bayesian inference for the Extended Plackett-Luce modelBayesian Analysis10.1214/21-BA125817:2Online publication date: 1-Jun-2022
https://doi.org/10.1214/21-BA1258
Nagy MMolontay R(2022)Network classification-based structural analysis of real networks and their model-generated counterpartsNetwork Science10.1017/nws.2022.1410:2(146-169)Online publication date: 20-May-2022
https://doi.org/10.1017/nws.2022.14
Pham TSheridan PShimodaira H(2021)Non-parametric estimation of the preferential attachment function from one network snapshotJournal of Complex Networks10.1093/comnet/cnab0249:5Online publication date: 29-Sep-2021
https://doi.org/10.1093/comnet/cnab024
Show More Cited By

Index Terms

Graph model selection using maximum likelihood
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
  2. Probability and statistics
    1. Statistical paradigms
      1. Statistical graphics
2. Networks
  1. Network properties
    1. Network structure

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cover image ACM Other conferences

ICML '06: Proceedings of the 23rd international conference on Machine learning

June 2006

1154 pages

ISBN:1595933832

DOI:10.1145/1143844

Program Chairs:
William Cohen,
Andrew Moore

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 25 June 2006

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ICML '06 Paper Acceptance Rate 140 of 548 submissions, 26%;

Overall Acceptance Rate 140 of 548 submissions, 26%

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Cited By

Johnson SHenderson DBoys R(2022)On Bayesian inference for the Extended Plackett-Luce modelBayesian Analysis10.1214/21-BA125817:2Online publication date: 1-Jun-2022
https://doi.org/10.1214/21-BA1258
Nagy MMolontay R(2022)Network classification-based structural analysis of real networks and their model-generated counterpartsNetwork Science10.1017/nws.2022.1410:2(146-169)Online publication date: 20-May-2022
https://doi.org/10.1017/nws.2022.14
Pham TSheridan PShimodaira H(2021)Non-parametric estimation of the preferential attachment function from one network snapshotJournal of Complex Networks10.1093/comnet/cnab0249:5Online publication date: 29-Sep-2021
https://doi.org/10.1093/comnet/cnab024
Dong JChen BZhang PAi CZhang FGuo DQiu X(2019)Evolution Model of Spatial Interaction Network in Online Social Networking ServicesEntropy10.3390/e2104043421:4(434)Online publication date: 24-Apr-2019
https://doi.org/10.3390/e21040434
Dong JChen BAi CZhang PQiu XHe L(2019)Data Driven Spatio-Info Network Modeling and Evolution With Population and EconomyIEEE Access10.1109/ACCESS.2019.29192567(77190-77199)Online publication date: 2019
https://doi.org/10.1109/ACCESS.2019.2919256
Gan LDjuric P(2017)Bayesian selection of models of network formation2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)10.1109/CAMSAP.2017.8313218(1-5)Online publication date: Dec-2017
https://doi.org/10.1109/CAMSAP.2017.8313218
(2017)Upper and lower bounds for the q-entropy of network models with application to network model selectionInformation Processing Letters10.1016/j.ipl.2016.11.002119:C(1-8)Online publication date: 1-Mar-2017
https://dl.acm.org/doi/10.1016/j.ipl.2016.11.002
Lee CGarbett AWilkinson D(2017)A network epidemic model for online community commissioning dataStatistics and Computing10.1007/s11222-017-9770-628:4(891-904)Online publication date: 2-Aug-2017
https://doi.org/10.1007/s11222-017-9770-6
Lefortier DOstroumova LSamosvat E(2013)Evolution of the Media WebAlgorithms and Models for the Web Graph10.1007/978-3-319-03536-9_7(80-92)Online publication date: 2013
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Leskovec JChakrabarti DKleinberg JFaloutsos CGhahramani Z(2010)Kronecker Graphs: An Approach to Modeling NetworksThe Journal of Machine Learning Research10.5555/1756006.175603911(985-1042)Online publication date: 1-Mar-2010
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