Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions

zbMath1467.62057arXiv1604.05251MaRDI QIDQ4558193

Carl-Johann Simon-Gabriel, Bernhard Schölkopf

Publication date: 21 November 2018

Full work available at URL: https://arxiv.org/abs/1604.05251

zbMATH Keywords

Schwartz distributionskernel mean embeddingcharacteristic kerneluniversal kernelkernel metrics on distributionsmetrisation of the weak topology

Mathematics Subject Classification ID

Density estimation (62G07) Weak and generalized continuity (54C08) Characterization and structure theory of statistical distributions (62E10) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Convergence of probability measures (60B10)

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Cites Work

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• On the optimal estimation of probability measures in weak and strong topologies
• Espaces de fonctions différentiables à valeurs vectorielles
• 10.1162/153244302760185252
• Hilbert space embeddings and metrics on probability measures
• VECTOR VALUED REPRODUCING KERNEL HILBERT SPACES OF INTEGRABLE FUNCTIONS AND MERCER THEOREM
• Support Vector Machines
• Algorithmic Learning Theory
• Universality, Characteristic Kernels and RKHS Embedding of Measures
• Bounded Measures on Topological Spaces
• Scattered Data Approximation