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Sparse Approximate Inference for Spatio-Temporal Point Process Models
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DOI：10.1080/01621459.2015.1115357.png)
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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.
Keyword:
Conflict analysis
Expectation propagation
Latent Gaussian models
Log-Gaussian Cox process
Sparse approximate inference
Structure learning
Variational approximate inference
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