Optimality of poisson processes intensity learning with Gaussian processes

Alisa Kirichenko, Harry Van Zanten

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a ddimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational approach and showed in simulation and real data experiments that it can work quite satisfactorily. The results presented in the present paper provide theoretical underpinning of the method. In particular, we show how to tune the priors on the hyper parameters of the model in order for the procedure to automatically adapt to the degree of smoothness of the unknown intensity, and to achieve optimal convergence rates.

Original languageEnglish
Pages (from-to)2909-2919
Number of pages11
JournalJournal of Machine Learning Research
Volume16
Publication statusPublished - 1 Dec 2015
Externally publishedYes

Keywords

  • Adaptation to smoothness
  • Bayesian intensity learning
  • Gaussian process prior
  • Inhomogeneous Poisson process
  • Optimal rates

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