Problem
Research questions and friction points this paper is trying to address.
Bayesian Optimization
Spatio-Temporal Data
Log-Gaussian Cox Process
Point Process
Scalability
ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach
🤖 AI Summary
This study addresses the bottleneck of standard Gaussian process-based Bayesian optimization in efficiently handling spatiotemporal doubly stochastic Cox processes by proposing the first scalable spatiotemporal Bayesian optimization framework. Methodologically, it employs a log-Gaussian Cox process to model the intensity function, integrating INLA-SPDE with Matérn field discretization to enable fast inference. Furthermore, a time-varying upper confidence bound acquisition strategy coupled with a masking mechanism is designed to prevent redundant evaluations. Experiments demonstrate that the proposed framework accurately locates peaks and recovers intensity fields on both synthetic and real-world datasets, achieving substantial computational speedups over reproducing kernel Hilbert space baselines while offering both theoretical novelty and practical utility.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bayesian Optimization
Log-Gaussian Cox Process
INLA-SPDE
Spatio-Temporal Modeling
Gaussian Markov Random Field
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