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={M. Driscoll},
  journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  year={1973},
  volume={26},
  pages={309-316}
}
  • M. Driscoll
  • Published 1973
  • Mathematics
  • Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
View on Springer
44 Citations
Highly Influential Citations
6
Background Citations
19
Methods Citations
4
Results Citations
1

44 Citations

Citation Type

Citation Type

Small Sample Spaces for Gaussian Processes
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
Learning Integral Representations of Gaussian Processes
TLDR
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
An RKHS formulation of the inverse regression dimension-reduction problem
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
Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences
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
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
A generalization of the randomized singular value decomposition
TLDR
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
Convergence of Gaussian process regression: Optimality, robustness, and relationship with kernel ridge regression.
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
Mixtures of Gaussian Processes for regression under multiple prior distributions
TLDR
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
A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges
TLDR
An overview and survey of several classes of Gaussian process constraints, including positivity or bound constraints, monotonicity and convexity constraints, differential equation constraints provided by linear PDEs, and boundary condition constraints are provided. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 10 REFERENCES
Continuity Properties of Some Gaussian Processes
Zero-one laws for Gaussian processes
Some zero-one laws are proved for Gaussian processes defined on linear spaces of functions. They are generalizations of a result for Wiener measure due to R. H. Cameron and R. E. Graves. The proofs… Expand
On the continuity of stationary Gaussian processes
Let us consider a stochastically continuous, separable and measurable stationary Gaussian process X = { X ( t ), − ∞ t ∞ } with mean zero and with the covariance function p ( t ) = EX ( t + s ) X ( s… Expand
Some properties of the measures on function spaces induced by Gaussian processes
Sample Functions of Gaussian Random Homogeneous Fields and Either Continuous or Very Irregular
Time Series Analysis Papers
Convergence of Random Processes and Limit Theorems in Probability Theory
The convergence of stochastic processes is defined in terms of the so-called “weak convergence” (w. c.) of probability measures in appropriate functional spaces (c. s. m. s.).Chapter 1. Let $\Re $ be… Expand
A theory of cross-spaces
Theory of Reproducing Kernels.
Abstract : The present paper may be considered as a sequel to our previous paper in the Proceedings of the Cambridge Philosophical Society, Theorie generale de noyaux reproduisants-Premiere partie… Expand
The Theory of Matrices