Related papers: Optimal design for kernel interpolation: applicati…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
Many local integral methods are based on an integral formulation over small and heavilly overlapping stencils with local RBF interpolations. These functions have become an extremely effective tool for interpolation on scattered node sets,…
We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with…
This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous…
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…
A number of basic image processing tasks, such as any geometric transformation require interpolation at subpixel image values. In this work we utilize the multidimensional coordinate Hermite spline interpolation defined on non-equal spaced,…
Point-wise localization of individual fluorophores is a critical step in super-resolution microscopy and single particle tracking. Although the methods are limited by the accuracy in localizing individual flourophores, this point-wise…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
This paper presents a class of Crank-Nicolson (CN) type schemes enhanced by radial basis function (RBF) interpolation for the time integration of linear parabolic partial differential equations (PDEs). The resulting RBF-CN schemes preserve…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…
Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of…
A novel search method for large polarization kernels is proposed. The algorithm produces a kernel with given partial distances by employing the depth-first search combined with the computation of coset leaders weight tables and sufficient…
In the preprocessing model for uncertain data we are given a set of regions R which model the uncertainty associated with an unknown set of points P. In this model there are two phases: a preprocessing phase, in which we have access only to…
This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…
This paper develops the process of using Richardson Extrapolation to improve the Kernel Density Estimation method, resulting in a more accurate (lower Mean Squared Error) estimate of a probability density function for a distribution of data…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
We introduce Soft Kernel Interpolation (SoftKI), a method that combines aspects of Structured Kernel Interpolation (SKI) and variational inducing point methods, to achieve scalable Gaussian Process (GP) regression on high-dimensional…
We investigate the spectrum of differentiation matrices for certain operators on the sphere that are generated from collocation at a set of scattered points $X$ with positive definite and conditionally positive definite kernels. We focus on…
While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…