IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v110y2023i1p15-32..html
   My bibliography  Save this article

Subsampling sparse graphons under minimal assumptions

Author

Listed:
  • Robert Lunde
  • Purnamrita Sarkar

Abstract

SummaryWe study the properties of two subsampling procedures for networks, vertex subsampling and $p$-subsampling, under the sparse graphon model. The consistency of network subsampling is demonstrated under the minimal assumptions of weak convergence of the corresponding network statistics and an expected subsample size growing to infinity more slowly than the number of vertices in the network. Furthermore, under appropriate sparsity conditions, we derive limiting distributions for the nonzero eigenvalues of an adjacency matrix under the sparse graphon model. Our weak convergence result implies the consistency of our subsampling procedures for eigenvalues under appropriate conditions.

Suggested Citation

  • Robert Lunde & Purnamrita Sarkar, 2023. "Subsampling sparse graphons under minimal assumptions," Biometrika, Biometrika Trust, vol. 110(1), pages 15-32.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:1:p:15-32.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asac032
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Rastelli, Riccardo & Friel, Nial & Raftery, Adrian E., 2016. "Properties of latent variable network models," Network Science, Cambridge University Press, vol. 4(4), pages 407-432, December.
    2. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    3. Traud, Amanda L. & Mucha, Peter J. & Porter, Mason A., 2012. "Social structure of Facebook networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4165-4180.
    4. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
    5. Patrick Rubin‐Delanchy & Joshua Cape & Minh Tang & Carey E. Priebe, 2022. "A statistical interpretation of spectral embedding: The generalised random dot product graph," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1446-1473, September.
    6. Harry Crane & Walter Dempsey, 2018. "Edge Exchangeable Models for Interaction Networks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1311-1326, July.
    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. Laleh Tafakori & Armin Pourkhanali & Riccardo Rastelli, 2022. "Measuring systemic risk and contagion in the European financial network," Empirical Economics, Springer, vol. 63(1), pages 345-389, July.
    2. Ick Hoon Jin & Minjeong Jeon, 2019. "A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 236-260, March.
    3. Bryan S. Graham, 2019. "Network Data," Papers 1912.06346, arXiv.org.
    4. François Caron & Emily B. Fox, 2017. "Sparse graphs using exchangeable random measures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1295-1366, November.
    5. Adrian E. Raftery, 2017. "Comment: Extending the Latent Position Model for Networks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1531-1534, October.
    6. Volfovsky, Alexander & Airoldi, Edoardo M., 2016. "Sharp total variation bounds for finitely exchangeable arrays," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 54-59.
    7. Peter D. Hoff, 2009. "Multiplicative latent factor models for description and prediction of social networks," Computational and Mathematical Organization Theory, Springer, vol. 15(4), pages 261-272, December.
    8. Hledik, Juraj & Rastelli, Riccardo, 2020. "A dynamic network model to measure exposure diversification in the Austrian interbank market," ESRB Working Paper Series 109, European Systemic Risk Board.
    9. Tracy Sweet & Samrachana Adhikari, 2020. "A Latent Space Network Model for Social Influence," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 251-274, June.
    10. S Chandna & S C Olhede & P J Wolfe, 2022. "Local linear graphon estimation using covariates [Representations for partially exchangeable arrays of random variables]," Biometrika, Biometrika Trust, vol. 109(3), pages 721-734.
    11. Juraj Hledik & Riccardo Rastelli, 2018. "A dynamic network model to measure exposure diversification in the Austrian interbank market," Papers 1804.01367, arXiv.org, revised Aug 2018.
    12. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model‐based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354, March.
    13. Xin Xu & Yang Lu & Yupeng Zhou & Zhiguo Fu & Yanjie Fu & Minghao Yin, 2021. "An Information-Explainable Random Walk Based Unsupervised Network Representation Learning Framework on Node Classification Tasks," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    14. Ian E. Fellows & Mark S. Handcock, 2023. "Modeling of networked populations when data is sampled or missing," METRON, Springer;Sapienza Università di Roma, vol. 81(1), pages 21-35, April.
    15. Yin, Mei, 2022. "Remarks on power-law random graphs," Stochastic Processes and their Applications, Elsevier, vol. 153(C), pages 183-197.
    16. Samrachana Adhikari & Beau Dabbs, 2018. "Social Network Analysis in R: A Software Review," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 225-253, April.
    17. Guang Ouyang & Dipak K. Dey & Panpan Zhang, 2020. "Clique-Based Method for Social Network Clustering," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 254-274, April.
    18. Thanne Mafaziya Nijamdeen & Jean Huge & Hajaniaina Ratsimbazafy & Kodikara Arachchilage Sunanda Kodikara & Farid Dahdouh-Guebas, 2022. "A social network analysis of mangrove management stakeholders in Sri Lanka's Northern Province," ULB Institutional Repository 2013/349602, ULB -- Universite Libre de Bruxelles.
    19. Yuan, Quan & Liu, Binghui, 2021. "Community detection via an efficient nonconvex optimization approach based on modularity," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    20. repec:hal:journl:hal-04672521 is not listed on IDEAS
    21. Samrachana Adhikari & Tracy Sweet & Brian Junker, 2021. "Analysis of longitudinal advice‐seeking networks following implementation of high stakes testing," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(4), pages 1475-1500, October.

    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:oup:biomet:v:110:y:2023:i:1:p:15-32.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.