Large-Scale Cox Process Inference using Variational Fourier Features
This enables large-scale, flexible modeling of spatiotemporal data for applications like ecology or epidemiology, representing a significant scaling advance over previous methods.
The paper tackles the problem of scaling Gaussian process modulated Poisson processes for spatiotemporal point patterns beyond small datasets and one-dimensional or gridded approximations, achieving the ability to fit over 100,000 events in three dimensions on a single GPU.
Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined 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 computationally efficient. This allows us to formulate a grid-free approximation that scales well with the number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. We also find that, in practice, 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.