mlsanityData to 7 Oct 2026

Characteristic kernels on Hilbert spaces, Banach spaces, and on sets of measures

arXiv 2206.07588 ↗First posted 15 Jun 2022stat.ML cs.LG math.FAcited by 7

Not on the map. Why?

Abstract (arXiv)

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes of kernels on Banach spaces and on metric spaces of strong negative type. The general results are used to give explicit classes of kernels on separable Lp spaces and on sets of measures.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 10 of its 49 references that are in the map. First posted on arXiv 15 Jun 2022.

Builds on

10 of 49 references.

References · 10

  1. 2014Learning Theory for Distribution Regressioncited by 48
  2. 2016Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributionscited by 39
  3. 2020Metrizing Weak Convergence with Maximum Mean Discrepanciescited by 35
  4. 2020A Kernel Two-Sample Test for Functional Datacited by 27
  5. 2019Quantitative stability of optimal transport maps and linearization of the 2-Wasserstein spacecited by 25
  6. 2015Generalized Spectral Kernelscited by 17
  7. 2019Function-Space Distributions over Kernelscited by 17
  8. 2017Strictly proper kernel scores and characteristic kernels on compact spacescited by 14
  9. 2019Kernels over Sets of Finite Sets using RKHS Embeddings, with Application to Bayesian (Combinatorial) Optimizationcited by 12
  10. 2021Marginalising over Stationary Kernels with Bayesian Quadraturecited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 5; 2026: 2.

7 papers.

  1. 2025Probabilistic neural operators for functional uncertainty quantificationcited by 17
  2. 2025Data Reliability Scoringcited by 2
  3. 2025Uncertainty Quantification for Regression: A Unified Framework based on kernel scorescited by 2
  4. 2025Kernel Quantile Embeddings and Associated Probability Metricscited by 0
  5. 2025Quantum-inspired probability metrics define a complete, universal space for statistical learningcited by 0
  6. 2026Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objectscited by 0
  7. 2026Improving Function Space Flow Matching with Kernel Optimal Transportcited by 0