# The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process

@article{Driscoll1973TheRK, title={The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process}, author={Michael F. Driscoll}, journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete}, year={1973}, volume={26}, pages={309-316} }

#### 46 Citations

Small Sample Spaces for Gaussian Processes

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- 2021

It is known that the membership in a given reproducing kernel Hilbert space (RKHS) of the samples of a Gaussian process X is controlled by a certain nuclear dominance condition. However, it is less… Expand

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The Gaussian process modeling is a standard tool for building emulators for computer experiments, which is usually a deterministic function, for example, solution to a partial differential equations… Expand

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The main innovation in the regression algorithm is the construction of a low dimensional subspace that captures the information most relevant to explaining variation in the response that uses ideas from supervised dimension reduction to compute this subspace. Expand

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Suppose that $Y$ is a scalar and $X$ is a second-order stochastic process, where $Y$ and $X$ are conditionally independent given the random variables $\xi_1,...,\xi_p$ which belong to the closed span… Expand

An optimal property of the best linear unbiased interpolation filter

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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

- Mathematics, Computer Science
- ArXiv
- 2018

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian… Expand

Stochastic Filtering on Shape Manifolds

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This thesis addresses the problem of learning the dynamics of deforming objects in image time series. In many biomedical imaging and computer vision applications it is important to satisfy certain… Expand

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- Computer Science, Mathematics
- ArXiv
- 2021

This work generalizes the theory of randomized SVD to multivariable Gaussian vectors, allowing one to incorporate prior knowledge of A into the algorithm, and constructs a new covariance kernel for GPs, based on weighted Jacobi polynomials. Expand

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In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly… Expand

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- Computer Science, Mathematics
- ArXiv
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The idea of Mixture models for Gaussian Process regression in order to work with multiple prior beliefs at once both a analytical regression formula and a Sparse Variational approach are considered. Expand

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