Optimality of Poisson processes intensity learning with Gaussian processes
This work offers theoretical underpinning for a computational method in point process modeling, which is incremental as it builds on prior empirical results.
The paper provides theoretical support for the Sigmoidal Gaussian Cox Process method for learning the intensity of inhomogeneous Poisson processes, showing how to tune hyperparameter priors to adapt to smoothness and achieve optimal convergence rates.
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 $d$-dimensional 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.