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[2602.16218] Bayesian Quadrature: Gaussian Processes for Integration
Summary
This article presents a comprehensive survey on Bayesian quadrature, a probabilistic approach to numerical integration, detailing its mathematical foundations, taxonomy, theoretical guarantees, and practical challenges.
Why It Matters
Bayesian quadrature is crucial for efficiently estimating complex integrals in various fields, including machine learning and engineering. This survey fills a significant gap in the literature by providing a systematic overview and addressing practical challenges, making it a valuable resource for researchers and practitioners.
Key Takeaways
- Bayesian quadrature offers a model-based approach to numerical integration.
- The article categorizes different Bayesian quadrature methods based on modeling, inference, and sampling.
- It provides theoretical guarantees and a numerical study to illustrate method effectiveness.
- Practical challenges in applying Bayesian quadrature methods are discussed.
- An extensive bibliography is included, covering relevant literature across multiple disciplines.
Computer Science > Machine Learning arXiv:2602.16218 (cs) [Submitted on 18 Feb 2026] Title:Bayesian Quadrature: Gaussian Processes for Integration Authors:Maren Mahsereci, Toni Karvonen View a PDF of the paper titled Bayesian Quadrature: Gaussian Processes for Integration, by Maren Mahsereci and 1 other authors View PDF HTML (experimental) Abstract:Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and comprehensive treatment has been published. The purpose of this survey is to fill this gap. We review the mathematical foundations of Bayesian quadrature from different points of view; present a systematic taxonomy for classifying different Bayesian quadrature methods along the three axes of modelling, inference, and sampling; collect general theoretical guarantees; and provide a controlled numerical study that explores and illustrates the effect of different choices along the axes of the taxonomy. We also provide a realistic assessment of practical challenges and limitations to application of Bayesian quadrature methods and include an up-to-date and nearly exhaustive bibliography that covers not only machine learning and statistics literature but all areas of mathematics and engineering in which Bayesian quadrature or equivalent methods have seen use. Subjects: Machine Learning (cs.LG); Numerical Analy...
