Tractable Nonparametric Bayesian Inference in Poisson Processes with Gaussian Process Intensities

Proceedings of the 26th International Conference on Machine Learning, Montreal, Canada (2009)
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Honorable Mention for Best Student Paper

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.

Keywords:

cox process, gaussian cox process, gaussian process, highlighted, point process, poisson process, time series