Related papers: Kernel-based interpolation at approximate Fekete p…
Kernel based approximation offers versatile tools for high-dimensional approximation, which can especially be leveraged for surrogate modeling. For this purpose, both "knot insertion" and "knot removal" approaches aim at choosing a suitable…
Meshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
Gaussian process regression is a classical kernel method for function estimation and data interpolation. In large data applications, computational costs can be reduced using low-rank or sparse approximations of the kernel. This paper…
The convergence rates on polynomial interpolation in most cases are estimated by Lebesgue constants. These estimates may be overestimated for some special points of sets for functions of limited regularities. In this paper, by applying the…
Given a point set $P\subset \mathbb{R}^d$, the kernel density estimate of $P$ is defined as \[ \overline{\mathcal{G}}_P(x) = \frac{1}{\left|P\right|}\sum_{p\in P}e^{-\left\lVert x-p \right\rVert^2} \] for any $x\in\mathbb{R}^d$. We study…
The generalization ability of kernel interpolation in large dimensions (i.e., $n \asymp d^{\gamma}$ for some $\gamma>0$) might be one of the most interesting problems in the recent renaissance of kernel regression, since it may help us…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
In this work, we propose an approach to perform non-uniform image interpolation based on a Gaussian Mixture Model. Traditional image interpolation methods, like nearest neighbor, bilinear, Hamming, Lanczos, etc. assume that the coordinates…
In this paper we discuss equidistribution results for weighted Fekete sets in subsets of the plane. More precisely, we show that Fekete sets are maximally spread out relative to a rescaled version of the Beurling--Landau density, in the…
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in effective algorithms that construct convex quadrature rules…
The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…
Using a lemma of Davis on Gram matrices applied to the classical Orthogonal Polynomials to generate reproducing kernel interpolation over the classical domains for polynomials. These kernels have terms which are exact over the rational…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…
Error estimates for kernel interpolation in Reproducing Kernel Hilbert Spaces (RKHS) usually assume quite restrictive properties on the shape of the domain, especially in the case of infinitely smooth kernels like the popular Gaussian…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
The k-point correlation functions of the Gaussian Random Matrix Ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We…