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Results tagged with hilbert-spaces
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user 58664
A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.
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Distribution of the RKHS norm of the posterior of a Gaussian process
In a classical noisy regression setting, let $\big(f(x)\big)_{x\in\cal X}$ be a centered Gaussian process of covariance $k$ on a compact $\cal X$, and $\mathcal{F}_n$ be the filtration generated by so …
- 183
4
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RKHS norm and posterior of Gaussian process
In Srinivas et al (2010) [appendix B], the authors claim the following "easy to see" property relating the norm of a function in a RKHS induced by a kernel $k(\cdot,\cdot)$, and its norm in the RKHS i …
- 183
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Distribution of the RKHS norm of the posterior of a Gaussian process
It is possible to get tail inequalities of such a quadratic form of a Gaussian vector using the results from (Hsu et al, 2012).
They prove that if $\rm C=A^\top A$ is a psd matrix and $\rm Y$ is a $\ …
- 183