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Sparse Approximate Inference for Spatio-Temporal Point Process Models

Author

Listed:
  • Botond Cseke
  • Andrew Zammit-Mangion
  • Tom Heskes
  • Guido Sanguinetti

Abstract

Spatio-temporal log-Gaussian Cox process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computationally challenging both due to the high-resolution modeling generally required and the analytically intractable likelihood function. Here, we exploit the sparsity structure typical of (spatially) discretized log-Gaussian Cox process models by using approximate message-passing algorithms. The proposed algorithms scale well with the state dimension and the length of the temporal horizon with moderate loss in distributional accuracy. They hence provide a flexible and faster alternative to both nonlinear filtering-smoothing type algorithms and to approaches that implement the Laplace method or expectation propagation on (block) sparse latent Gaussian models. We infer the parameters of the latent Gaussian model using a structured variational Bayes approach. We demonstrate the proposed framework on simulation studies with both Gaussian and point-process observations and use it to reconstruct the conflict intensity and dynamics in Afghanistan from the WikiLeaks Afghan War Diary. Supplementary materials for this article are available online.

Suggested Citation

  • Botond Cseke & Andrew Zammit-Mangion & Tom Heskes & Guido Sanguinetti, 2016. "Sparse Approximate Inference for Spatio-Temporal Point Process Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1746-1763, October.
  • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:516:p:1746-1763
    DOI: 10.1080/01621459.2015.1115357
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    Cited by:

    1. Andrew Zammit‐Mangion, 2020. "Discussion on A high‐resolution bilevel skew‐t stochastic generator for assessing Saudi Arabia's wind energy resources," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    2. Michael E Rule & David Schnoerr & Matthias H Hennig & Guido Sanguinetti, 2019. "Neural field models for latent state inference: Application to large-scale neuronal recordings," PLOS Computational Biology, Public Library of Science, vol. 15(11), pages 1-23, November.
    3. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.

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