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

62 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
Country/TerritoryCanada
CityMontreal, QC
Period6/14/096/18/09

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

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