mlsanityData to 7 Oct 2026

On Average-Case Error Bounds for Kernel-Based Bayesian Quadrature

arXiv 2202.10615 ↗First posted 22 Feb 2022stat.ML cs.IT cs.LGcited by 3

Not on the map. Why?

Abstract (arXiv)

In this paper, we study error bounds for em Bayesian quadrature (BQ), with an emphasis on noisy settings, randomized algorithms, and average-case performance measures. We seek to approximate the integral of functions in a em Reproducing Kernel Hilbert Space (RKHS), particularly focusing on the Mat'ern-nu and squared exponential (SE) kernels, with samples from the function potentially being corrupted by Gaussian noise. We provide a two-step meta-algorithm that serves as a general tool for relating the average-case quadrature error with the L2-function approximation error. When specialized to the Mat'ern kernel, we recover an existing near-optimal error rate while avoiding the existing method of repeatedly sampling points. When specialized to other settings, we obtain new average-case results for settings including the SE kernel with noise and the Mat'ern kernel with misspecification. Finally, we present algorithm-independent lower bounds that have greater generality and/or give distinct proofs compared to existing ones.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 14 of its 48 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

14 of 48 references.

References · 14

  1. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
  2. 2020On Information Gain and Regret Bounds in Gaussian Process Banditscited by 156
  3. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  4. 2017Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimizationcited by 77
  5. 2021Optimal Order Simple Regret for Gaussian Process Banditscited by 52
  6. 2020Bandit optimisation of functions in the Mat'ern kernel RKHScited by 40
  7. 2019An Introductory Guide to Fano's Inequality with Applications in Statistical Estimationcited by 30
  8. 2020Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothnesscited by 29
  9. 2020On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimizationcited by 29
  10. 2018But How Does It Work in Theory? Linear SVM with Random Featurescited by 28
  11. 2019Convergence Guarantees for Adaptive Bayesian Quadrature Methodscited by 22
  12. 2019Active Multi-Information Source Bayesian Quadraturecited by 17
2 more
  1. 2020Multi-Scale Zero-Order Optimization of Smooth Functions in an RKHScited by 16
  2. 2016Convergence guarantees for kernel-based quadrature rules in misspecified settingscited by 15

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2025Nested Expectations with Kernel Quadraturecited by 5
  2. 2024Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimizationcited by 2
  3. 2026Envy-Free Allocation of Indivisible Goods via Noisy Queriescited by 0