Large-Scale Cox Process Inference using Variational Fourier Features

TL;DR

This paper introduces a scalable, grid-free Bayesian inference method for large-scale spatiotemporal Cox processes using Fourier features, enabling efficient modeling of complex point patterns in high dimensions.

Contribution

The paper presents a novel Fourier feature-based approach for Cox process inference that scales to over 100,000 events and offers more stable optimization than previous methods.

Findings

Enables modeling of large spatiotemporal datasets with over 100,000 points.

Provides a grid-free, computationally efficient inference method.

Demonstrates improved optimization stability over prior approaches.

Abstract

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.