Bayesian optimization method speeds up spatio-temporal location searches
ISBO: Scalable Spatio-Temporal Bayesian Optimization with Log Gaussian Cox Process Models via the INLA-SPDE Approach
Machine Learning
Summary
Finding the best spots in space and time for certain events can be very slow and complicated. The authors created a new way to do this faster by modeling events as random points that change over time and space. They use advanced math tools to make predictions and quickly find important spots without checking everywhere. Their method uses less computing power and works better than older ones in tests.
What this means in practice
- •For environmental monitoring teams: Identify hotspots of environmental events over time and space rapidly with fewer data checks.
- •For urban planners: Locate areas with rising or peak incidents for better resource distribution using spatio-temporal modeling.
Authors
Kaichuang Yang, Håvard Rue, Jakob Zeitler
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.