Sparse Approximate Inference for Spatio-Temporal Point Process Models

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.