Gamma Gaussian Cox Processes
Christian Walder, Adrian N. Bishop · arXiv (Cornell University) · 2017
The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. Much work has focused on the Log-Gaussian Cox process, where the logarithm of the intensity is a Gaussian process. In this paper we propose the Gamma Gaussian Cox Process, under which the square root of the intensity is a Gaussian process. This formulation admits analytical simplifications via connections with reproducing kernel Hilbert spaces, which we leverage here to derive efficient approximate Bayesian inference algorithms. We derive the Laplace approximation to the predictive distribution and marginal likelihood, and demonstrate the practical utility of the approximation on toy and real-world problems.