Sparse Approximate Inference for Spatio-Temporal Point Process Models
This work addresses the problem of computationally intensive inference for researchers and practitioners in fields like conflict analysis, offering a faster alternative to existing methods, though it is incremental as it builds on known sparsity structures and variational approaches.
The paper tackled the computational challenge of scalable inference in spatio-temporal point process models by developing approximate message-passing algorithms that exploit sparsity, resulting in algorithms that scale well with state dimension and temporal horizon with moderate accuracy loss, as demonstrated in simulation studies and an application to conflict intensity reconstruction in Afghanistan.
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling generally required and the analytically intractable likelihood function. Here, we exploit the sparsity structure typical of (spatially) discretised 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 non-linear 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.