Tractable Nonparametric Bayesian Inference in Poisson Processes with Gaussian Process Intensities

Adams, R. P., Murray, I., & MacKay, D. J. C. (2009). Tractable Nonparametric Bayesian Inference in Poisson Processes with Gaussian Process Intensities. Proceedings of the 26th International Conference on Machine Learning (ICML).

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.

  @conference{adams2009poisson,
  year = {2009},
  author = {Adams, Ryan P. and Murray, Iain and MacKay, David J.C.},
  title = {Tractable Nonparametric {B}ayesian Inference in {P}oisson Processes with {G}aussian Process Intensities},
  booktitle = {Proceedings of the 26th International Conference on Machine Learning (ICML)},
  location = {Montr{\'e}al, Canada},
  keywords = {Gaussian processes, Bayesian nonparametrics, Poisson processes, Bayesian methods, Markov chain Monte Carlo, time series, ICML}
}