PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Tractable Nonparametric Bayesian Inference in Poisson Processes with Gaussian Process Intensities
Ryan Adams, Iain Murray and David MacKay
Proceedings of the 26th Annual International Conference on Machine Learning pp. 9-16, 2009.

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 finitedimensional 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.

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EPrint Type:Article
Additional Information:Honourable mention for best student paper at ICML 2009
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:6583
Deposited By:Ryan Adams
Deposited On:08 March 2010