Related papers: Distributed Uncertainty Quantification of Kernel I…
To predict smooth physical phenomena from observations, spline interpolation provides an interpretable framework by minimizing an energy functional associated with the Laplacian operator. This work proposes a methodology to construct a…
We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main…
Interpolation models are critical for a wide range of applications, from numerical optimization to artificial intelligence. The reliability of the provided interpolated value is of utmost importance, and it is crucial to avoid the…
In many fields of science, comprehensive and realistic computational models are available nowadays. Often, the respective numerical calculations call for the use of powerful supercomputers, and therefore only a limited number of cases can…
We present a method for computing uncertainties in spectral models, i.e. level populations, line emissivities, and emission line ratios, based upon the propagation of uncertainties originating from atomic data. We provide analytic…
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…
The Partition of Unity (PU) method, performed with local Radial Basis Function (RBF) approximants, has been proved to be an effective tool for solving large scattered data interpolation problems. However, in order to achieve a good…
Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…
Thepaperprovesconvergenceofone-levelandmultilevelunsymmetriccollocationforsecondorderelliptic boundary value problems on the bounded domains. By using Schaback's linear discretization theory,L2 errors are obtained based on the kernel-based…
Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then…
We consider a distributed function computation problem in which parties observing noisy versions of a remote source facilitate the computation of a function of their observations at a fusion center through public communication. The…
This paper studies the influence of scaling on the behavior of Radial Basis Function interpolation. It focuses on certain central aspects, but does not try to be exhaustive. The most important questions are: How does the error of a…
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…
We study the problem of distributed Kalman filtering for sensor networks in the presence of model uncertainty. More precisely, we assume that the actual state-space model belongs to a ball, in the Kullback-Leibler topology, about the…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
Calibration is an essential step in radio interferometric data processing that corrects the data for systematic errors and in addition, subtracts bright foreground interference to reveal weak signals hidden in the residual. These weak and…
We construct $\bf genRBF$ kernel, which generalizes the classical Gaussian RBF kernel to the case of incomplete data. We model the uncertainty contained in missing attributes making use of data distribution and associate every point with a…
A method of interpolating the acoustic transfer function (ATF) between regions that takes into account both the physical properties of the ATF and the directionality of region configurations is proposed. Most spatial ATF interpolation…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
Accurate prediction of molecular vibrational frequencies is important to identify spectroscopic signatures and reaction thermodynamics. In this work, we develop a method to quantify uncertainty associated with density functional theory…