mlsanityData to 7 Oct 2026

Kernel quadrature with DPPs

arXiv 1906.07832 ↗First posted 18 Jun 2019stat.ML cs.LGcited by 26

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Abstract (arXiv)

We study quadrature rules for functions from an RKHS, using nodes sampled from a determinantal point process (DPP). DPPs are parametrized by a kernel, and we use a truncated and saturated version of the RKHS kernel. This link between the two kernels, along with DPP machinery, leads to relatively tight bounds on the quadrature error, that depends on the spectrum of the RKHS kernel. Finally, we experimentally compare DPPs to existing kernel-based quadratures such as herding, Bayesian quadrature, or leverage score sampling. Numerical results confirm the interest of DPPs, and even suggest faster rates than our bounds in particular cases.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 3; 2023: 9; 2024: 2; 2025: 6; 2026: 3.

26 papers.

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  1. 2021Kernel Thinningcited by 47
  2. 2021Positively Weighted Kernel Quadrature via Subsamplingcited by 25
  3. 2022Nystr"om Kernel Mean Embeddingscited by 21
  4. 2022Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombinationcited by 20
  5. 2022Sharp Analysis of Sketch-and-Project Methods via a Connection to Randomized Singular Value Decompositioncited by 17
  6. 2023Sampling-based Nystr"om Approximation and Kernel Quadraturecited by 17
  7. 2023Optimally-Weighted Estimators of the Maximum Mean Discrepancy for Likelihood-Free Inferencecited by 13
  8. 2023Kernel quadrature with randomly pivoted Choleskycited by 11
  9. 2023Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Samplingcited by 10
  10. 2025Weighted quantization using MMD: From mean field to mean shift via gradient flowscited by 10
  11. 2025A Dictionary of Closed-Form Kernel Mean Embeddingscited by 9
  12. 2023Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approachcited by 6
14 more
  1. 2025Nested Expectations with Kernel Quadraturecited by 5
  2. 2023When can Regression-Adjusted Control Variates Help? Rare Events, Sobolev Embedding and Minimax Optimalitycited by 4
  3. 2024A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Liftingcited by 3
  4. 2021Sparse solutions of the kernel herding algorithm by improved gradient approximationcited by 2
  5. 2023Signal reconstruction using determinantal samplingcited by 2
  6. 2024On the design of scalable, high-precision spherical-radial Fourier featurescited by 2
  7. 2025Stationary MMD Pointscited by 2
  8. 2023Policy Gradient with Kernel Quadraturecited by 1
  9. 2026Bayesian Quadraturecited by 1
  10. 2026To discretize continually: Mean shift interacting particle systems for Bayesian inferencecited by 1
  11. 2023Fast Empirical Scenarioscited by 0
  12. 2025Quenched large deviations for Monte Carlo integration with Coulomb gasescited by 0
  13. 2025Learning Geometric-Aware Quadrature Rules for Functional Minimizationcited by 0
  14. 2026Convex-Geometric Error Bounds for Positive-Weight Kernel Quadraturecited by 0