Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities

Ryan Prescott Adams, Iain Murray, David J.C. MacKay

Research output: Chapter in Book/Report/Conference proceedingConference contribution

64 Scopus citations

Abstract

The inhomogeneous Poisson process is a point process that has varying intensity across its domain (usually time or space). For nonparametric Bayesian modeling, the Gaussian process is a useful way to place a prior distribution on this intensity. The combination of a Poisson process and GP is known as a Gaussian Cox process, or doubly-stochastic Poisson process. Likelihood-based inference in these models requires an intractable integral over an infinite-dimensional random function. In this paper we present the first approach to Gaussian Cox processes in which it is possible to perform inference without introducing approximations or finite-dimensional proxy distributions. We call our method the Sigmoidal Gaussian Cox Process, which uses a generative model for Poisson data to enable tractable inference via Markov chain Monte Carlo. We compare our methods to competing methods on synthetic data and apply it to several real-world data sets.

Original languageEnglish (US)
Title of host publicationProceedings of the 26th International Conference On Machine Learning, ICML 2009
Pages9-16
Number of pages8
StatePublished - Dec 9 2009
Externally publishedYes
Event26th International Conference On Machine Learning, ICML 2009 - Montreal, QC, Canada
Duration: Jun 14 2009Jun 18 2009

Publication series

NameProceedings of the 26th International Conference On Machine Learning, ICML 2009

Other

Other26th International Conference On Machine Learning, ICML 2009
CountryCanada
CityMontreal, QC
Period6/14/096/18/09

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

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