发表机构
KAUST; University of Oxford（阿卜杜拉国王科技大学; 牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对时空数据的贝叶斯优化问题，提出首个可扩展框架ISBO，采用LGCP建模、INLA-SPDE推断，实验显示其峰值发现与强度恢复准确且速度显著提升，是点过程数据BO的实用方案。
AI 中文摘要
贝叶斯优化（BO）是一种用于高效优化昂贵黑盒目标的流行方法，但利用标准高斯过程的BO不适用于时空问题空间中常用的双重随机Cox过程。我们提出INLA-SPDE时空贝叶斯优化（ISBO）：首个针对时空数据的可扩展BO框架，其使用对数高斯Cox过程（LGCP）建模对数强度，并通过集成嵌套拉普拉斯近似与随机偏微分方程（INLA-SPDE）方法进行推断。在网格上使用Matern场生成稀疏高斯马尔可夫随机场，INLA在序贯优化中提供快速准确的后验推断。ISBO以最少的评估稳定定位高强度区域和潜在强度的峰值，带掩码的时变上置信边界采集避免重复访问，惩罚复杂度先验对早期轮次进行正则化。在合成和真实时空数据集上的实验表明，ISBO能准确发现峰值、恢复强度，且相比基于RKHS的基线实现了显著加速，使其成为处理点过程数据BO的实用选择。
英文摘要
Bayesian Optimization (BO) is a popular method for efficiently optimizing expensive black-box objectives. However, BO utilizing standard Gaussian Processes is ill-suited for doubly stochastic Cox Processes that are often used in spatio-temporal problem spaces. We introduce INLA-SPDE Spatio-Temporal Bayesian Optimization (ISBO): the first scalable BO framework for spatio-temporal data, that models the log-intensity with a Log-Gaussian Cox Process(LGCP) and performs inference via Integrated Nested Laplace Approximation and Stochastic Partial Differential Equations (INLA-SPDE) approach. Using a Matern field on meshes yields a sparse Gaussian Markov Random Field, where INLA provides fast and accurate posterior inference throughout sequential optimization. ISBO stably locates high-intensity regions and the peak of the latent intensity with minimal evaluations. A time-varying Upper Confidence Bound acquisition with masking avoids revisits, while penalized-complexity priors regularize early rounds. Experiments on synthetic and real-world spatio-temporal datasets show accurate peak discovery, intensity recovery, and substantial speedups over an RKHS-based baseline, positioning ISBO as a practical choice for BO with point-process data.
