mlsanityData to 7 Oct 2026

Kernelized Normalizing Constant Estimation: Bridging Bayesian Quadrature and Bayesian Optimization

arXiv 2401.05716 ↗First posted 11 Jan 2024cs.LG stat.MLcited by 2

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Abstract (arXiv)

In this paper, we study the problem of estimating the normalizing constant int e-λ f(x)dx through queries to the black-box function f, where f belongs to a reproducing kernel Hilbert space (RKHS), and λ is a problem parameter. We show that to estimate the normalizing constant within a small relative error, the level of difficulty depends on the value of λ: When λ approaches zero, the problem is similar to Bayesian quadrature (BQ), while when λ approaches infinity, the problem is similar to Bayesian optimization (BO). More generally, the problem varies between BQ and BO. We find that this pattern holds true even when the function evaluations are noisy, bringing new aspects to this topic. Our findings are supported by both algorithm-independent lower bounds and algorithmic upper bounds, as well as simulation studies conducted on a variety of benchmark functions.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 22 of its 38 references that are in the map. First posted on arXiv 11 Jan 2024.

Builds on

22 of 38 references.

References · 22

  1. 2017On Kernelized Multi-armed Banditscited by 348
  2. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
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  6. 2017Lower Bounds on Regret for Noisy Gaussian Process Bandit Optimizationcited by 77
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  9. 2022Towards a Theory of Non-Log-Concave Sampling: First-Order Stationarity Guarantees for Langevin Monte Carlocited by 63
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  11. 2021Optimal Order Simple Regret for Gaussian Process Banditscited by 52
  12. 2020Non-parametric Models for Non-negative Functionscited by 40
10 more
  1. 2020Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothnesscited by 29
  2. 2020On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimizationcited by 29
  3. 2019Convergence Guarantees for Adaptive Bayesian Quadrature Methodscited by 22
  4. 2019Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Boundscited by 16
  5. 2016Poisson intensity estimation with reproducing kernelscited by 14
  6. 2022Fisher information lower bounds for samplingcited by 12
  7. 2023Convergence Rates for Non-Log-Concave Sampling and Log-Partition Estimationcited by 10
  8. 2017Normalizing constants of log-concave densitiescited by 5
  9. 2022On Average-Case Error Bounds for Kernel-Based Bayesian Quadraturecited by 3
  10. 2021Invariant Priors for Bayesian Quadraturecited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Bayesian Quadraturecited by 1
  2. 2026Active Learning for Gaussian Process Regression Under Self-Induced Boltzmann Weightscited by 0