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Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations

arXiv 2609.08813 ↗First posted 8 Sep 2026stat.AP stat.ME stat.MLcited by 0

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Abstract (arXiv)

We study continuous-time relational event data, where time-stamped dyadic interactions reflect both individual node propensities and evolving relational proximity. We propose a dynamic latent space model for inhomogeneous Poisson processes, where event intensities depend on node-specific activity parameters and time-varying latent distances modeled via flexible B-splines. We prove model identifiability by decoupling baseline activity from latent position, ensuring high interaction volumes do not warp the spatial map. For scalability, we develop a minibatch stochastic gradient algorithm with stable initialization and geometric anchoring, alongside an effective-degrees-of-freedom BIC for tuning model complexity. Simulations confirm accurate parameter recovery and out-of-sample prediction. Applied to cooperative diplomatic events among 60 major economies (1995--2022), the model uncovers shifting patterns of international cooperation and isolates mobile geopolitical actors from stationary institutional anchors.

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References · 14

  1. 2020Latent Space Models for Dynamic Networkscited by 29
  2. 2016Bayesian Poisson Tucker Decomposition for Learning the Structure of International Relationscited by 25
  3. 2015Bayesian Poisson Tensor Factorization for Inferring Multilateral Relations from Sparse Dyadic Event Countscited by 19
  4. 2015A semiparametric extension of the stochastic block model for longitudinal networkscited by 10
  5. 2022A Mutually Exciting Latent Space Hawkes Process Model for Continuous-time Networkscited by 10
  6. 2013Nonparametric Bayes dynamic modeling of relational datacited by 8
  7. 2021Continuous Latent Position Models for Instantaneous Interactionscited by 8
  8. 2015Locally Adaptive Dynamic Networkscited by 7
  9. 2020Network Hawkes Process Models for Exploring Latent Hierarchy in Social Animal Interactionscited by 4
  10. 2022Dynamic latent space relational event modelcited by 4
  11. 2024Gaussian Embedding of Temporal Networkscited by 3
  12. 2022Latent process models for functional network datacited by 2
2 more
  1. 2023Semiparametric Modeling and Analysis for Longitudinal Network Datacited by 1
  2. 2024Fast Variational Inference of Latent Space Models for Dynamic Networks Using Bayesian P-Splinescited by 1

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