mlsanityData to 7 Oct 2026

Positively Weighted Kernel Quadrature via Subsampling

arXiv 2107.09597 ↗First posted 20 Jul 2021math.NA cs.LG cs.NAcited by 25

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Abstract (arXiv)

We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules using only access to i.i.d. samples from the underlying measure and evaluation of the kernel and that result in a small worst-case error. In addition to our theoretical results and the benefits resulting from convex weights, our experiments indicate that this construction can compete with the optimal bounds in well-known examples.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 16 of its 84 references that are in the map. First posted on arXiv 20 Jul 2021.

Builds on

16 of 84 references.

References · 16

  1. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  2. 2015On the Equivalence between Kernel Quadrature Rules and Random Feature Expansionscited by 136
  3. 2020Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyondcited by 107
  4. 2014Control functionals for Monte Carlo integrationcited by 59
  5. 2021Kernel Thinningcited by 47
  6. 2019Kernel quadrature with DPPscited by 26
  7. 2020Kernel interpolation with continuous volume samplingcited by 21
  8. 2015Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guaranteescited by 20
  9. 2017Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settingscited by 16
  10. 2016Convergence guarantees for kernel-based quadrature rules in misspecified settingscited by 15
  11. 2016Black-box Importance Samplingcited by 13
  12. 2018A Bayes-Sard Cubature Methodcited by 10
4 more
  1. 2020Semi-Exact Control Functionals From Sard's Methodcited by 9
  2. 2020A Randomized Algorithm to Reduce the Support of Discrete Measurescited by 6
  3. 2020A Statistical Perspective on Coreset Density Estimationcited by 6
  4. 2016Methods for Sparse and Low-Rank Recovery under Simplex Constraintscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 11; 2024: 1; 2025: 6; 2026: 5.

25 papers.

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  1. 2023Looping in the Human Collaborative and Explainable Bayesian Optimizationcited by 27
  2. 2022Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombinationcited by 20
  3. 2023Sampling-based Nystr"om Approximation and Kernel Quadraturecited by 17
  4. 2023Kernel quadrature with randomly pivoted Choleskycited by 11
  5. 2023Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Samplingcited by 10
  6. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 10
  7. 2022Bayesian Model Selection of Lithium-Ion Battery Models via Bayesian Quadraturecited by 8
  8. 2023SOBER: Highly Parallel Bayesian Optimization and Bayesian Quadrature over Discrete and Mixed Spacescited by 7
  9. 2023Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approachcited by 6
  10. 2026WildCat: Near-Linear Attention in Theory and Practicecited by 6
  11. 2025Nested Expectations with Kernel Quadraturecited by 5
  12. 2023When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimalitycited by 4
13 more
  1. 2024A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Liftingcited by 3
  2. 2025Stationary MMD Pointscited by 2
  3. 2025Theoretical Refinement of CLIP by Utilizing Linear Structure of Optimal Similaritycited by 2
  4. 2023Bayesian Quadrature for Neural Ensemble Searchcited by 1
  5. 2023Compressed online Sinkhorncited by 1
  6. 2023Policy Gradient with Kernel Quadraturecited by 1
  7. 2025Solving the Cold Start Problem on One's Own as an End User via Preference Transfercited by 1
  8. 2026Bayesian Quadraturecited by 1
  9. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  10. 2023Fast Empirical Scenarioscited by 0
  11. 2025BayesSum: Bayesian Quadrature in Discrete Spacescited by 0
  12. 2026Convex-Geometric Error Bounds for Positive-Weight Kernel Quadraturecited by 0
  13. 2026Amortized quadrature for posterior expectations in inverse problemscited by 0