Variational Inference for Gaussian Process Modulated Poisson Processes

TL;DR

This paper introduces a fully variational Bayesian inference method for Gaussian-process-modulated Poisson processes that is computationally efficient, scalable, and outperforms existing methods in various applications.

Contribution

It is the first to provide a fully variational inference scheme for these processes, eliminating the need for domain discretization and significantly improving speed.

Findings

Outperforms standard methods on synthetic data

Achieves faster inference than sampling approaches

Successfully predicts Malaria incidences in Kenya

Abstract

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Our scheme: requires no discretisation of the domain; scales linearly in the number of observed events; and is many orders of magnitude faster than previous sampling based approaches. The resulting algorithm is shown to outperform standard methods on synthetic examples, coal mining disaster data and in the prediction of Malaria incidences in Kenya.