Gaussian Processes and Reproducing Kernels: Connections and Equivalences
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913905034395648 |
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| author | Kanagawa, Motonobu Hennig, Philipp Sejdinovic, Dino Sriperumbudur, Bharath K. |
| author_facet | Kanagawa, Motonobu Hennig, Philipp Sejdinovic, Dino Sriperumbudur, Bharath K. |
| contents | This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences between them are reviewed for fundamental topics such as regression, interpolation, numerical integration, distributional discrepancies, and statistical dependence, as well as for sample path properties of Gaussian processes. A unifying perspective for these equivalences is established, based on the equivalence between the Gaussian Hilbert space and the RKHS. The monograph serves as a basis to bridge many other methods based on Gaussian processes and reproducing kernels, which are developed in parallel by the two research communities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian Processes and Reproducing Kernels: Connections and Equivalences Kanagawa, Motonobu Hennig, Philipp Sejdinovic, Dino Sriperumbudur, Bharath K. Machine Learning Numerical Analysis Probability Statistics Theory This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences between them are reviewed for fundamental topics such as regression, interpolation, numerical integration, distributional discrepancies, and statistical dependence, as well as for sample path properties of Gaussian processes. A unifying perspective for these equivalences is established, based on the equivalence between the Gaussian Hilbert space and the RKHS. The monograph serves as a basis to bridge many other methods based on Gaussian processes and reproducing kernels, which are developed in parallel by the two research communities. |
| title | Gaussian Processes and Reproducing Kernels: Connections and Equivalences |
| topic | Machine Learning Numerical Analysis Probability Statistics Theory |
| url | https://arxiv.org/abs/2506.17366 |