Sparse Approximate Inference for Spatio-Temporal Point Process Models

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.

Keywords:

• Conflict analysis
• Expectation propagation
• Latent Gaussian models
• Log-Gaussian Cox process
• Sparse approximate inference
• Structure learning
• Variational approximate inference

Funding

B. Cs. was funded by BBSRC under grant BB/I004777/1. A. Z.-M. was partially funded by NERC under grant NE/I027401/1 while at the University of Bristol. Guido Sanguinetti was funded by ERC under grant MLCS-306999.

Notes

1 See supplementary material for details.

2 http://www.mathworks.com

3 All algorithms were tested on an Intel Core™i7-2600S @ 2.80 GHz personal computer with 8 GB of RAM.