# Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Data

arXiv: https://arxiv.org/abs/2401.14544 · HTML: https://mlsanity.com/paper/2401.14544/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 25 Jan 2024.

## Builds on (most cited first, 19 of 19)

- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Every Parameter Matters: Ensuring the Convergence of Federated Learning with Dynamic Heterogeneous Models Reduction](https://mlsanity.com/paper/2310.08670/) (2023)
- [MAC-PO: Multi-Agent Experience Replay via Collective Priority Optimization](https://mlsanity.com/paper/2302.10418/) (2023)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Poisson intensity estimation with reproducing kernels](https://mlsanity.com/paper/1610.08623/) (2016)
- [A Bayesian Optimization Framework for Finding Local Optima in Expensive Multi-Modal Functions](https://mlsanity.com/paper/2210.06635/) (2022)
- [Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search](https://mlsanity.com/paper/1705.04405/) (2017)
- [Fast Bayesian Intensity Estimation for the Permanental Process](https://mlsanity.com/paper/1701.03535/) (2017)
- [Scalable Multi-agent Covering Option Discovery based on Kronecker Graphs](https://mlsanity.com/paper/2307.11629/) (2023)
- [Structured Variational Inference in Continuous Cox Process Models](https://mlsanity.com/paper/1906.03161/) (2019)
- [Particle-based Online Bayesian Sampling](https://mlsanity.com/paper/2302.14796/) (2023)
- [AccMER: Accelerating Multi-Agent Experience Replay with Cache Locality-aware Prioritization](https://mlsanity.com/paper/2306.00187/) (2023)
- [Knowledge Distillation Circumvents Nonlinearity for Optical Convolutional Neural Networks](https://mlsanity.com/paper/2102.13323/) (2021)
- [Efficient Bayesian Nonparametric Modelling of Structured Point Processes](https://mlsanity.com/paper/1407.6949/) (2014)
- [Bayesian Hyperparameter Optimization for Deep Neural Network-Based Network Intrusion Detection](https://mlsanity.com/paper/2207.09902/) (2022)
- [Federated Conditional Stochastic Optimization](https://mlsanity.com/paper/2310.02524/) (2023)
- [Exploiting Partial Common Information Microstructure for Multi-Modal Brain Tumor Segmentation](https://mlsanity.com/paper/2302.02521/) (2023)

## Built on by (most cited first, 5 of 5)

- [Auto-Train-Once: Controller Network Guided Automatic Network Pruning from Scratch](https://mlsanity.com/paper/2403.14729/) (2024)
- [Collaborative AI Teaming in Unknown Environments via Active Goal Deduction](https://mlsanity.com/paper/2403.15341/) (2024)
- [MALinZero: Efficient Low-Dimensional Search for Mastering Complex Multi-Agent Planning](https://mlsanity.com/paper/2511.06142/) (2025)
- [RGMDT: Return-Gap-Minimizing Decision Tree Extraction in Non-Euclidean Metric Space](https://mlsanity.com/paper/2410.16517/) (2024)
- [Global Optimization on Graph-Structured Data via Gaussian Processes with Spectral Representations](https://mlsanity.com/paper/2511.07734/) (2025)

## Abstract (arXiv)

Bayesian optimization (BO) has established itself as a leading strategy for efficiently optimizing expensive-to-evaluate functions. Existing BO methods mostly rely on Gaussian process (GP) surrogate models and are not applicable to (doubly-stochastic) Gaussian Cox processes, where the observation process is modulated by a latent intensity function modeled as a GP. In this paper, we propose a novel maximum a posteriori inference of Gaussian Cox processes. It leverages the Laplace approximation and change of kernel technique to transform the problem into a new reproducing kernel Hilbert space, where it becomes more tractable computationally. It enables us to obtain both a functional posterior of the latent intensity function and the covariance of the posterior, thus extending existing works that often focus on specific link functions or estimating the posterior mean. Using the result, we propose a BO framework based on the Gaussian Cox process model and further develop a Nystr"om approximation for efficient computation. Extensive evaluations on various synthetic and real-world datasets demonstrate significant improvement over state-of-the-art inference solutions for Gaussian Cox processes, as well as effective BO with a wide range of acquisition functions designed through the underlying Gaussian Cox process model.