Bayesian Quadrature

arXiv:2602.16218 · cs.LG, cs.NA, math.NA, stat.ML · Submitted 2026-02-18 · Read on arXiv

cs.LG, cs.NA, math.NA, stat.ML

Submitted: 2026-02-18

Updated: 2026-09-16

Comments: 131 pages

Journal ref: Maren Mahsereci and Toni Karvonen (2026), "Bayesian Quadrature", Foundations and Trends in Machine Learning: Vol. 19, No. 2-3, pp 121-240

DOI: 10.1108/FTMAL-06-2026-0132

Code: https://github.com/mmahsereci/kernel_embedding_dictionary

Project page: http://gailgithub.github.io/GAIL_Dev

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Acquisition Function — 37× in this paper · explained in 1 episode
• Calibration — 31× in this paper · explained in 7 episodes
• Hilbert Space — 25× in this paper · explained in 2 episodes
• Theoretical Guarantees — 21× in this paper · explained in 2 episodes
• Bayesian Optimization — 12× in this paper · explained in 3 episodes
• Accuracy — 9× in this paper · explained in 1 episode
• Bayesian Monte Carlo — 9× in this paper
• Embeddings — 9× in this paper · explained in 2 episodes
• Uncertainty Quantification — 9× in this paper · explained in 8 episodes
• Bayesian Inference — 6× in this paper · explained in 5 episodes
• Convergence Guarantees — 6× in this paper · explained in 3 episodes
• Fidelity — 5× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Active Learning — 2× in this paper · explained in 6 episodes
• Computational Tractability — 2× in this paper · explained in 2 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Bayesian Optimization (BO) — 1× in this paper · explained in 3 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Frustration — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 3 episodes
• Sample Efficiency — 1× in this paper · explained in 4 episodes
• Steering — 1× in this paper · explained in 2 episodes

Sources

• Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach
• On Average-Case Error Bounds for Kernel-Based Bayesian Quadrature
• Bayesian Quadrature for Neural Ensemble Search
• BINOCULARS for Efficient, Nonmyopic Sequential Experimental Design
• Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences
• BayesSum: Bayesian Quadrature in Discrete Spaces
• General superconvergence for kernel-based approximation
• An Active Learning Reliability Method for Systems with Partially Defined Performance Functions
• Kernel quadrature by applying a point-wise gradient descent method to discrete energies
• Sparse solutions of the kernel herding algorithm by improved gradient approximation
• Batch Selection for Parallelisation of Bayesian Quadrature
• ProbNum: Probabilistic Numerics in Python

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