mlsanityData to 7 Oct 2026

Nested Expectations with Kernel Quadrature

arXiv 2502.18284 ↗First posted 25 Feb 2025stat.ML cs.LGcited by 5

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Abstract (arXiv)

This paper considers the challenging computational task of estimating nested expectations. Existing algorithms, such as nested Monte Carlo or multilevel Monte Carlo, are known to be consistent but require a large number of samples at both inner and outer levels to converge. Instead, we propose a novel estimator consisting of nested kernel quadrature estimators and we prove that it has a faster convergence rate than all baseline methods when the integrands have sufficient smoothness. We then demonstrate empirically that our proposed method does indeed require fewer samples to estimate nested expectations on real-world applications including Bayesian optimisation, option pricing, and health economics.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 39 of its 102 references that are in the map. First posted on arXiv 25 Feb 2025.

Builds on

39 of 102 references.

References · 39

  1. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  2. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 188
  3. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  4. 2023Modern Bayesian Experimental Designcited by 121
  5. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
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  7. 2014Control functionals for Monte Carlo integrationcited by 59
  8. 2019Deep learning is adaptive to intrinsic dimensionality of model smoothness in anisotropic Besov spacecited by 46
  9. 2016Parallel Bayesian Global Optimization of Expensive Functionscited by 43
  10. 2015GLASSES: Relieving The Myopia Of Bayesian Optimisationcited by 38
  11. 2014Sampling for Inference in Probabilistic Models with Fast Bayesian Quadraturecited by 31
  12. 2020Convergence Guarantees for Gaussian Process Means With Misspecified Likelihoods and Smoothnesscited by 29
27 more
  1. 2015Probabilistic Integration: A Role in Statistical Computation?cited by 26
  2. 2019Kernel quadrature with DPPscited by 26
  3. 2021Positively Weighted Kernel Quadrature via Subsamplingcited by 25
  4. 2019Convergence Guarantees for Adaptive Bayesian Quadrature Methodscited by 22
  5. 2015Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guaranteescited by 20
  6. 2023On the Optimality of Misspecified Kernel Ridge Regressioncited by 20
  7. 2019A Kernel Stein Test for Comparing Latent Variable Modelscited by 18
  8. 2019Active Multi-Information Source Bayesian Quadraturecited by 17
  9. 2023Sampling-based Nystr"om Approximation and Kernel Quadraturecited by 17
  10. 2017Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settingscited by 16
  11. 2021Bayesian Distributionally Robust Optimizationcited by 16
  12. 2024(De)-regularized Maximum Mean Discrepancy Gradient Flowcited by 14
  13. 2018Multilevel Monte Carlo estimation of expected information gainscited by 13
  14. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  15. 2021Vector-Valued Control Variatescited by 12
  16. 2023Kernel quadrature with randomly pivoted Choleskycited by 11
  17. 2020Scalable Control Variates for Monte Carlo Methods via Stochastic Optimizationcited by 10
  18. 2021ProbNum: Probabilistic Numerics in Pythoncited by 10
  19. 2018Symmetry Exploits for Bayesian Cubature Methodscited by 8
  20. 2022Multilevel Bayesian Quadraturecited by 8
  21. 2024Conditional Bayesian Quadraturecited by 8
  22. 2017On the Sampling Problem for Kernel Quadraturecited by 7
  23. 2024Nonparametric Instrumental Regression via Kernel Methods is Minimax Optimalcited by 7
  24. 2018Optimal Learning with Anisotropic Gaussian SVMscited by 4
  25. 2024Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Needcited by 4
  26. 2022On Average-Case Error Bounds for Kernel-Based Bayesian Quadraturecited by 3
  27. 2024Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Setscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 2.

5 papers.

  1. 2025Multilevel neural simulation-based inferencecited by 5
  2. 2026Sobolev Regularized MMD Gradient Flowcited by 3
  3. 2025Stationary MMD Pointscited by 2
  4. 2026Bayesian Quadraturecited by 1
  5. 2025BayesSum: Bayesian Quadrature in Discrete Spacescited by 0