# ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach

arXiv: https://arxiv.org/abs/2610.12213 · HTML: https://mlsanity.com/paper/2610.12213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 45 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 2 of 2)

- [A Study of Bayesian Neural Network Surrogates for Bayesian Optimization](https://mlsanity.com/paper/2305.20028/) (2023)
- [Collaborative AI Teaming in Unknown Environments via Active Goal Deduction](https://mlsanity.com/paper/2403.15341/) (2024)

## Abstract (arXiv)

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.