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.

本文提出了一种新颖的基于高斯 Cox 过程的最大后验推断方法，通过引入 Laplace 近似和核函数转换技术，使得推断问题在新的再生核希尔伯特空间中更易于计算，从而在功能后验和后验的协方差方面得到了扩展。在此基础上，我们提出了一个基于高斯 Cox 过程模型的贝叶斯优化框架，并进一步开发了一种 Nyström 近似方法以进行高效计算。在各种合成和实际数据集上的广泛评估表明，与现有的高斯 Cox 过程推断解决方案相比，本方法取得了显著的改进，同时还能有效地进行基于高斯 Cox 过程模型设计的各种收集函数的贝叶斯优化。