arXiv：cs.LG· Kaichuang Yang, H{\aa}vard Rue, Jakob Zeitler·· 3 小时前
ISBO：基于 INLA-SPDE 与 Log-Gaussian Cox Process 的可扩展时空贝叶斯优化
ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach
AI 导读
ISBO 是首个面向时空数据的可扩展贝叶斯优化框架，用 Log-Gaussian Cox Process 建模对数强度，并通过 INLA-SPDE 做推断。它借助 Matern 场在网格上生成稀疏高斯马尔可夫随机场，实现快速准确的后验推断，配合带掩码的时变 Upper Confidence Bound 采集函数避免重复访问。
正文
Abstract: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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.12213 [stat.ML] |
| (or arXiv:2610.12213v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.12213 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Kaichuang Yang [view email]
[v1]
Thu, 8 Oct 2026 16:01:37 UTC (9,286 KB)
来源：arXiv：cs.LG · arxiv.org