CUED Publications database

Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities

Adams, RP and Murray, I and MacKay, DJC (2009) Tractable nonparametric Bayesian inference in Poisson processes with Gaussian process intensities. Proceedings of the 26th International Conference On Machine Learning, ICML 2009. pp. 9-16.

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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.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Machine Intelligence
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 12:05
Last Modified: 08 Dec 2014 02:23
DOI: