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Nonparametric Bayes dynamic modelling of relational data

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  • Daniele Durante
  • David B. Dunson

Abstract

Symmetric binary matrices representing relations are collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being on inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By using a logistic mapping function from the link probability matrix space to the latent relational space, we obtain a flexible and computationally tractable formulation. Employing Pólya-gamma data augmentation, an efficient Gibbs sampler is developed for posterior computation, with the dimension of the latent space automatically inferred. We provide theoretical results on flexibility of the model, and illustrate its performance via simulation experiments. We also consider an application to co-movements in world financial markets.

Suggested Citation

  • Daniele Durante & David B. Dunson, 2014. "Nonparametric Bayes dynamic modelling of relational data," Biometrika, Biometrika Trust, vol. 101(4), pages 883-898.
  • Handle: RePEc:oup:biomet:v:101:y:2014:i:4:p:883-898.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu040
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    Cited by:

    1. Wei, Fengrong & Tian, Weizhong, 2018. "Heterogeneous connection effects," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 9-14.
    2. Christian U Carmona & Serafin Martinez-Jaramillo, 2019. "Learning of Weighted Dynamic Multi-layer Networks via Latent Gaussian Processes," Post-Print hal-02213097, HAL.
    3. 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.
    4. Turnbull, Kathryn & Nemeth, Christopher & Nunes, Matthew & McCormick, Tyler, 2023. "Sequential estimation of temporally evolving latent space network models," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    5. Michael Schweinberger, 2020. "Statistical inference for continuous‐time Markov processes with block structure based on discrete‐time network data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 342-362, August.
    6. Bartolucci, Francesco & Marino, Maria Francesca & Pandolfi, Silvia, 2015. "Composite likelihood inference for hidden Markov models for dynamic networks," MPRA Paper 67242, University Library of Munich, Germany.
    7. Linardi, Fernando & Diks, Cees & van der Leij, Marco & Lazier, Iuri, 2020. "Dynamic interbank network analysis using latent space models," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    8. Federica Bianchi & Francesco Bartolucci & Stefano Peluso & Antonietta Mira, 2020. "Longitudinal networks of dyadic relationships using latent trajectories: evidence from the European interbank market," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 711-739, August.
    9. Raffaele Argiento & Matteo Ruggiero, 2018. "Computational challenges and temporal dependence in Bayesian nonparametric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 231-238, June.
    10. 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.
    11. Ahelegbey, Daniel Felix & Giudici, Paolo & Hadji-Misheva, Branka, 2019. "Latent factor models for credit scoring in P2P systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 112-121.
    12. Sosa, Juan & Betancourt, Brenda, 2022. "A latent space model for multilayer network data," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    13. Fengrong Wei, 2018. "A Short Discussion of Network Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 12-13, June.
    14. Owen G. Ward & Jing Wu & Tian Zheng & Anna L. Smith & James P. Curley, 2022. "Network Hawkes process models for exploring latent hierarchy in social animal interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1402-1426, November.
    15. Daniel Felix Ahelegbey & Luis Carvalho & Eric D. Kolaczyk, 2020. "A Bayesian Covariance Graph And Latent Position Model For Multivariate Financial Time Series," DEM Working Papers Series 181, University of Pavia, Department of Economics and Management.
    16. Calissano, Anna & Feragen, Aasa & Vantini, Simone, 2022. "Graph-valued regression: Prediction of unlabelled networks in a non-Euclidean graph space," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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