Scattered Data Approximation

By M. Urner. 2016

1,692 citations recorded by the source corpus.

Subfields: Numerical Methods & Scientific Computing

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In Numerical Methods & Scientific Computing

Citations in the corpus

Consistent Kernel Mean Estimation for Functions of Random Variables (2016, methodology): “Then F ψ(ω) = (1 + ‖ω‖22)−s2 (Wendland, 2004, Chapter 10).”
Minimax Estimation of Kernel Mean Embeddings (2016, background): “To this end, since ψ ∧ ∈ L1(Rd), Fourier inversion theorem (Wendland, 2005, Corollary 5.24) yields that for all x ∈ Rd, the following holds: ψ(x) = 1 (2π)d/2 ∫ Rd ei〈w,x〉ψ∧(w)dw.”
Optimal Rates for Random Fourier Features (2015, background): “We also propose a RFF approximation to derivatives of a kernel with a theoretical study on its approximation quality.”
Kernel Mean Shrinkage Estimators (2014, background): “The following result provides an alternate expression for the score, which can be evaluated eﬃciently.”
Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “A desirable property for representing probability distributions P ∈ P(X ) in an RKHS H is that different probability distributions P,Q ∈ P(X ), P 6= Q map to different elements mP 6= mQ in the RKHS H, i.e., the kernel mean map P 7→ mP is injective.”
Density Estimation in Infinite Dimensional Exponential Families (2013, neutral): “e with λ= n−max{ 1 3 , 1 2(β+1) }. If kC−1k <∞, then the result follows by noting k √ C(fλ,n− f0)kH ≤ k √ Ckkfλ,n−f0kH and invoking the bound in (21). 8.7 Proof of Proposition 8 Observation 1: By (Wendland, 2005, Theorem 10.12), we have H= ˆ f∈ L2(Rd)∩Cb(Rd) : f∧ √ ψ∧ ∈ L2(Rd) ˙ , where f∧ is deﬁ”
On the optimal estimation of probability measures in weak and strong topologies (2013, methodology): “Similar to the Gaussian kernel family, it can be shown that b where the deﬁnition of · H α follows from [39, Theorems 6.13 and 10.12].”
Scalable Kernel Methods via Doubly Stochastic Gradients (2014, background): “Instead of ﬁnding the random processes P ( ω ) and functions φ ω ( x ) given kernels, one can go the reverse direction and construct kernels from random processes and functions ( e.g. , Wendland [18]).”
Convergence rates for a class of estimators based on Stein’s method (2016, background): “7 of [45] where an overview of the strengths and weaknesses of results in the scattered data approximation literature is provided.”
Review on computational methods for Lyapunov functions (2015, methodology): “Buhmann 2003 [47] and Wendland 2005 [225].”
Support points (2016, background): “43 of [72] shows that Gp is indeed equal to the Sobolev 16”
A Geometric Comparison of Aerofoil Shape Parameterisation Methods (2016, methodology): “The general theory of RBFs is outlined by Wendland[45] and Buhmann[46]; the formulation used here is presented extensively in Rendall and Allen[11] and its use as a parametrisation technique in Morris et al.”