IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v171y2022ics0167947322000299.html
   My bibliography  Save this article

Hybrid maximum likelihood inference for stochastic block models

Author

Listed:
  • Marino, Maria Francesca
  • Pandolfi, Silvia

Abstract

Stochastic block models have known a flowering interest in the social network literature. They provide a tool for discovering communities and identifying clusters of individuals characterized by similar social behaviors. In this framework, full maximum likelihood estimates are not achievable due to the intractability of the likelihood function. For this reason, several approximate solutions are available in the literature. In this respect, a new and more efficient approximate method for estimating model parameters is introduced. This has a hybrid nature, in the sense that it exploits different features of existing methods. The proposal is illustrated by an intensive Monte Carlo simulation study and an application to a real-world network.

Suggested Citation

  • Marino, Maria Francesca & Pandolfi, Silvia, 2022. "Hybrid maximum likelihood inference for stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:csdana:v:171:y:2022:i:c:s0167947322000299
    DOI: 10.1016/j.csda.2022.107449
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322000299
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107449?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Christophe Ambroise & Catherine Matias, 2012. "New consistent and asymptotically normal parameter estimates for random‐graph mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 3-35, January.
    2. McDaid, Aaron F. & Murphy, Thomas Brendan & Friel, Nial & Hurley, Neil J., 2013. "Improved Bayesian inference for the stochastic block model with application to large networks," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 12-31.
    3. Etienne Côme & Nicolas Jouvin & Pierre Latouche & Charles Bouveyron, 2021. "Hierarchical clustering with discrete latent variable models and the integrated classification likelihood," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 957-986, December.
    4. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    5. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
    6. Timothée Tabouy & Pierre Barbillon & Julien Chiquet, 2020. "Variational Inference for Stochastic Block Models From Sampled Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 455-466, January.
    7. Bartolucci, Francesco & Marino, Maria Francesca & Pandolfi, Silvia, 2018. "Dealing with reciprocity in dynamic stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 86-100.
    8. Catherine Matias & Vincent Miele, 2017. "Statistical clustering of temporal networks through a dynamic stochastic block model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1119-1141, September.
    9. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ludkin, Matthew, 2020. "Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    2. Riccardo Rastelli & Michael Fop, 2020. "A stochastic block model for interaction lengths," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 485-512, June.
    3. Dragana M. Pavlović & Bryan R.L. Guillaume & Soroosh Afyouni & Thomas E. Nichols, 2020. "Multi‐subject stochastic blockmodels with mixed effects for adaptive analysis of individual differences in human brain network cluster structure," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 363-396, August.
    4. Bartolucci, Francesco & Marino, Maria Francesca & Pandolfi, Silvia, 2018. "Dealing with reciprocity in dynamic stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 86-100.
    5. Chabert-Liddell, Saint-Clair & Barbillon, Pierre & Donnet, Sophie & Lazega, Emmanuel, 2021. "A stochastic block model approach for the analysis of multilevel networks: An application to the sociology of organizations," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    6. Volodymyr Melnykov & Xuwen Zhu, 2019. "An extension of the K-means algorithm to clustering skewed data," Computational Statistics, Springer, vol. 34(1), pages 373-394, March.
    7. Francesco Dotto & Alessio Farcomeni & Luis Angel García-Escudero & Agustín Mayo-Iscar, 2017. "A fuzzy approach to robust regression clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 691-710, December.
    8. Pierre Barbillon & Sophie Donnet & Emmanuel Lazega & Avner Bar-Hen, 2017. "Stochastic block models for multiplex networks: an application to a multilevel network of researchers," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 295-314, January.
    9. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.
    10. Rocci, Roberto & Vichi, Maurizio, 2008. "Two-mode multi-partitioning," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1984-2003, January.
    11. Sharon M. McNicholas & Paul D. McNicholas & Daniel A. Ashlock, 2021. "An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 264-279, July.
    12. Paul Riverain & Simon Fossier & Mohamed Nadif, 2023. "Poisson degree corrected dynamic stochastic block model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 135-162, March.
    13. Roberto Mari & Salvatore Ingrassia & Antonio Punzo, 2023. "Local and Overall Deviance R-Squared Measures for Mixtures of Generalized Linear Models," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 233-266, July.
    14. Aghiles Salah & Mohamed Nadif, 2019. "Directional co-clustering," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 591-620, September.
    15. Saint‐Clair Chabert‐Liddell & Pierre Barbillon & Sophie Donnet, 2022. "Impact of the mesoscale structure of a bipartite ecological interaction network on its robustness through a probabilistic modeling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.
    16. Shuchismita Sarkar & Volodymyr Melnykov & Rong Zheng, 2020. "Gaussian mixture modeling and model-based clustering under measurement inconsistency," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 379-413, June.
    17. Heath, Jeffrey W. & Fu, Michael C. & Jank, Wolfgang, 2009. "New global optimization algorithms for model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3999-4017, October.
    18. Hofmeyr, David P., 2020. "Degrees of freedom and model selection for k-means clustering," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    19. Catherine Matias & Vincent Miele, 2017. "Statistical clustering of temporal networks through a dynamic stochastic block model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1119-1141, September.
    20. Govaert, Gérard & Nadif, Mohamed, 2008. "Block clustering with Bernoulli mixture models: Comparison of different approaches," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3233-3245, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:171:y:2022:i:c:s0167947322000299. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.