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This paper introduces ISBO, a scalable framework for Bayesian Optimization tailored to spatio-temporal data using Log-Gaussian Cox Processes and the INLA-SPDE approach. By leveraging sparse Gaussian Markov Random Fields, it achieves efficient peak discovery with minimal evaluations, addressing limitations of standard Gaussian Process models in doubly stochastic settings. The method demonstrates significant speedups over existing baselines while maintaining accuracy on both synthetic and real-world datasets.
ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach
arXiv:2610.12213v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2610.12213 [stat.ML]
(or arXiv:2610.12213v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2610.12213 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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