ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach
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.
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BibTeX
@misc{yang2026isbo,
title = {{ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach}},
author = {Kaichuang Yang and Håvard Rue and Jakob Zeitler},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12213},
eprint = {2610.12213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12213},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach
AU - Kaichuang Yang
AU - Håvard Rue
AU - Jakob Zeitler
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.12213
UR - https://arxiv.org/abs/2610.12213
AB - 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.
ER -