Bayesian Optimization through Gaussian Cox Process Models for
  Spatio-temporal Data
Yongsheng Mei Mahdi Imani Tian Lan
Bayesian optimization (BO) has established itself as a leading strategy for
efficiently optimizing expensive-to-evaluate functions. Existing BO methods
mostly rely on Gaussian process (GP) surrogate models and are not applicable to
(doubly-stochastic) Gaussian Cox processes, where the observation process is
modulated by a latent intensity function modeled as a GP. In this paper, we
propose a novel maximum a posteriori inference of Gaussian Cox processes. It
leverages the Laplace approximation and change of kernel technique to transform
the problem into a new reproducing kernel Hilbert space, where it becomes more
tractable computationally. It enables us to obtain both a functional posterior
of the latent intensity function and the covariance of the posterior, thus
extending existing works that often focus on specific link functions or
estimating the posterior mean. Using the result, we propose a BO framework
based on the Gaussian Cox process model and further develop a Nystr\"om
approximation for efficient computation. Extensive evaluations on various
synthetic and real-world datasets demonstrate significant improvement over
state-of-the-art inference solutions for Gaussian Cox processes, as well as
effective BO with a wide range of acquisition functions designed through the
underlying Gaussian Cox process model.