Bayesian Optimization Framework Enhances Gaussian Process Kernel Selection

Global: Bayesian Optimization Framework Enhances Gaussian Process Kernel Selection

Researchers introduced a new Bayesian optimization approach for choosing covariance kernels in Gaussian Process (GP) regression in a preprint posted to arXiv in January 2026. The method targets the computational bottleneck of kernel selection by treating kernels as points in a geometric space and applying optimization techniques to improve predictive performance worldwide.

Background on Gaussian Process Regression

GP regression is a widely used non‑parametric Bayesian technique that models data through a prior distribution defined by a covariance kernel. The choice of kernel directly influences the model’s ability to capture underlying patterns, making kernel selection a critical yet resource‑intensive step in many applications.

Kernel‑of‑Kernels Geometry

The authors propose a “kernel‑of‑kernels” framework that quantifies similarity between GP priors using expected divergence‑based distances. By computing a distance matrix across a discrete library of candidate kernels, the approach creates a metric space that reflects functional relationships among kernels.

Embedding Kernels into a Continuous Manifold

To enable smooth optimization, the distance matrix is embedded into a Euclidean manifold via multidimensional scaling (MDS). This transformation maps each discrete kernel to a continuous coordinate vector, preserving geometric relationships when the divergence metric is valid.

Bayesian Optimization Process

Within the embedded space, the input domain consists of kernel compositions represented by their MDS coordinates. The optimization objective is the log marginal likelihood of the GP model, and the Bayesian optimizer searches the manifold to identify kernel configurations that maximize this likelihood.

Empirical Evaluation

The framework was tested on synthetic benchmarks, several real‑world time‑series datasets, and an additive manufacturing case study that predicts melt‑pool geometry. Across these experiments, the method achieved higher predictive accuracy and better uncertainty calibration than conventional baselines.

Comparative Performance

Results indicate that the proposed approach outperformed standard kernel search techniques, including a recent Large Language Model‑guided search, demonstrating both efficiency and robustness in diverse modeling scenarios.

Broader Impact and Future Work

By establishing a reusable probabilistic geometry for kernel exploration, the study offers a scalable tool for GP modeling and deep kernel learning. The authors suggest extending the methodology to larger kernel libraries and integrating it with automated machine learning pipelines.

This report is based on information from arXiv, licensed under Academic Preprint / Open Access. Based on the abstract of the research paper. Full text available via ArXiv.