Large-Scale Cox Process Inference using Variational Fourier Features

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Large-Scale Cox Process Inference using Variational Fourier Features

July 10 - 15, 2018 Stockholm International Fairs, Stockholm, Sweden

Thirty-fifth International Conference on Machine Learning (ICML 2018)

Authors: S.T. (, James Hensman (

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 behaviour than previous approaches. Our approximate Bayesian method can fit over 100,000 events with complex spatiotemporal patterns in three dimensions on a single GPU.

Gaussian Processes

Bayesian Optimisation

Probabilistic Modelling

See paper

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