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

DOI10.3150/23-bej1639arXiv2206.07588OpenAlexW4391458296WikidataQ128817781 ScholiaQ128817781MaRDI QIDQ6201859

David Ginsbourger, Johanna F. Ziegel, Lutz Dümbgen

Publication date: 26 March 2024

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.07588

zbMATH Keywords

characteristic kernelintegrally strictly positive definite kernelkernel on Banach spacekernel on Hilbert spacekernel on measures

Mathematics Subject Classification ID

Density estimation (62G07) Learning and adaptive systems in artificial intelligence (68T05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Topological data analysis (62R40)

Cites Work

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• Measuring and testing dependence by correlation of distances
• Equivalence of distance-based and RKHS-based statistics in hypothesis testing
• Distance covariance in metric spaces
• Mercer's theorem on general domains: on the interaction between measures, kernels, and RKHSs
• A new test for multivariate normality
• The geometry of proper scoring rules
• Kernel methods in machine learning
• Brownian distance covariance
• Uniqueness theorems for measures in \(L_ r\) and \(C_ o(\Omega)\)
• Positive definite functions and generalizations, an historical survey
• The small ball theorem for Hilbert spaces
• Interpolation of spatial data. Some theory for kriging
• On a new multivariate two-sample test.
• Ball divergence: nonparametric two sample test
• Gaussian processes with multidimensional distribution inputs via optimal transport and Hilbertian embedding
• Strictly proper kernel scores and characteristic kernels on compact spaces
• 10.1162/153244302760185252
• Learning Theory for Distribution Regression
• Hilbert space embeddings and metrics on probability measures
• Support Vector Machines
• Scoring Rules for Continuous Probability Distributions
• Gaussian Measures on Function Spaces
• Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions
• Distance covariance for stochastic processes
• An Invitation to Statistics in Wasserstein Space
• Strictly Proper Scoring Rules, Prediction, and Estimation
• Algorithmic Learning Theory
• Bimeasurable functions
• Functional analysis
• Scattered Data Approximation
• Measure and integration theory. Transl. from the German by Robert B. Burckel