Sparse Approximate Inference for Spatio-Temporal Point Process Models

• 成果类型: Article
• 署名作者: Cseke, Botond; Zammit-Mangion, Andrew; Heskes, Tom; Sanguinetti, Guido
• 署名单位: University of Edinburgh; University of Bristol; Radboud University Nijmegen
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1115357
• 发表日期: 2016
• 页码: 1746-1763
• 关键词: bayesian-inference; nested-dissection; patterns; diffusion; disease; systems; graphs

摘要

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.