Sparse Approximate Inference for Spatio-Temporal Point Process Models

TL;DR

This paper introduces scalable, approximate message-passing algorithms for inference in high-dimensional spatio-temporal point process models, enabling efficient analysis of complex spatial data with minimal accuracy loss.

Contribution

It presents a novel sparse inference framework using message passing and structured variational Bayes for high-dimensional spatio-temporal point processes.

Findings

Algorithms scale well with state dimension and time horizon.

Effective reconstruction of conflict intensity in Afghanistan.

Demonstrated accuracy on simulated and real-world data.

Abstract

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.