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Time-varying degree-corrected stochastic block models

Author

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  • Li, Mengxue

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • von Sachs, Rainer

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Pircalabelu, Eugen

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

Recent interest has emerged in community detection for dynamic networks which are observed along a trajectory of points in time. In this paper, we present a time-varying degree-corrected stochastic block model to fit a dynamic network which allows evolving heterogeneity in the degrees of nodes within a community over time. Considering the influence of the varying time window on the aggregation of network information from different time points, in the parameter estimation, we propose a smoothing-based method to recover time-varying degree parameters and communities. We also provide rates of consistency of our smoothed estimators for degree parameters and communities using a time-localised profile- likelihood approach. Extensive simulation studies and applications to two different real data sets complete our work.

Suggested Citation

  • Li, Mengxue & von Sachs, Rainer & Pircalabelu, Eugen, 2024. "Time-varying degree-corrected stochastic block models," LIDAM Discussion Papers ISBA 2024014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2024014
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    References listed on IDEAS

    as
    1. Srijan Sengupta & Yuguo Chen, 2018. "A block model for node popularity in networks with community structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 365-386, March.
    2. Jing Lei & Kehui Chen & Brian Lynch, 2020. "Consistent community detection in multi-layer network data," Biometrika, Biometrika Trust, vol. 107(1), pages 61-73.
    3. Jiangzhou Wang & Jingfei Zhang & Binghui Liu & Ji Zhu & Jianhua Guo, 2023. "Fast Network Community Detection With Profile-Pseudo Likelihood Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1359-1372, April.
    4. 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.
    5. Jing Lei & Kevin Z. Lin, 2023. "Bias-Adjusted Spectral Clustering in Multi-Layer Stochastic Block Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2433-2445, October.
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    More about this item

    Keywords

    Dynamic network ; Community detection ; Time-localised profile-likelihood ; Nonparametric curve estimation;
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