An Explicit Description of the Reproducing Kernel Hilbert Spaces of Gaussian RBF Kernels

By Ingo Steinwart, Don R. Hush, Clint Scovel. 2006

290 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Optimal a priori balance in the design of controlled experiments (2013, background): “−‖x−x′‖2/: the corresponding RKHS is infinite dimensional (non-parametric) and was studied in Steinwart et al. (2006).”
Fast rates for support vector machines using Gaussian kernels (2007, unknown): “18 38 v1 [ m at h. ST ] 1 4 A ug 2 00 7 The Annals of Statistics 2007, Vol. 35, No. 2, 575–607 DOI: 10.1214/009053606000001226 In the Public Domain”
Residual Weighted Learning for Estimating Individualized Treatment Rules (2015, unknown): “Hσ(Rp) be the RKHS of the Gaussian RBF kernel Kσ. The linear operator Vσ : L2(Rp) → Hσ(Rp) deﬁned by Vσℓ(x) = (2σ)d/2 πd/4 Z Rp e−2σ2||x−y||2ℓ(y)dy, ℓ ∈ L 2(R p), x ∈ Rp, is an isometric isomorphism (Steinwart et al. 2006). Thus we have, A(λ) ≤ inf ℓ∈L2(Rp) λ 2 ||ℓ||2 L2(Rp) +RT,g(Vσℓ)−R ∗ T,g. (27)”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “, 24, which are orthonormal in H(κ) (Steinwart et al., 2006).”
Consistency and Convergence Rates of One-Class SVM and Related Algorithms (2005, background): “In particular the consistency and convergence rates of the two-class SVM (see, e.g., Steinwart, 2002; Zhang, 2004; Steinwart and Scovel, 2004, and references therein) have been studied in detail, as well as the shape of the asymptotic decision function (Steinwart, 2003; Bartlett and Tewari, 2004).”
Benchmarking for Steganography (2008, unknown): “by providing its orthonormal (ON) basis [41]”
From Predictive to Prescriptive Analytics (2014, background): “s the previous or the exponential kernel K(x;x0) = e xT 0, which can be seen as its innite-dimensional limit. (c) The Gaussian kernel K s(x;x0) = e s 2 jjx0 2 (the corresponding space His studied in [38]). In both cases the restrictions on the norm are equivalent to incorporating an appropriately-we”
Reproducing Kernel Hilbert Spaces Associated with Analytic Translation-Invariant Mercer Kernels (2008, methodology): “A detailed analysis of the Gaussian case has been done in [ 17 ].”