Abstract

Gaussian process modulated Poisson processes provide a flexible framework for modeling spatiotemporal point patterns. So far this was restricted to one dimension, binning to a predetermined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier features. This sparse representation induces global rather than local constraints on the function space and is com putationally efficient. This allows us to formulat a grid-free approximation that scales well with th number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. In practice we find that Fourier features have more consistent optimization behavior than previous approaches. Our approximate Bayesian method can fit over 100 000 events with complex spatiotemporal patterns in three dimensions on a single GPU.