Related papers: Rational kernel-based interpolation for complex-va…
The performance of reproducing kernel Hilbert space-based methods is known to be sensitive to the choice of the reproducing kernel. Choosing an adequate reproducing kernel can be challenging and computationally demanding, especially in…
We present a number of new piecewise-polynomial kernels for image interpolation. The kernels are constructed by optimizing a measure of interpolation quality based on the magnitude of anisotropic artifacts. The kernel design process is…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
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…
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 is devoted to the study of vector valued reproducing kernel Hilbert spaces. We focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular we extend reproducing kernels to relative reproducing…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for…
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. We here unveil an analogy with…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
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…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
Recent advances in representation learning reveal that widely used objectives, such as contrastive and non-contrastive, implicitly perform spectral decomposition of a contextual kernel, induced by the relationship between inputs and their…
Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i.e., functionals). In this paper, we…
We develop and analyze a class of matrix-valued spherical-convolution kernels stemming from scaled zonal functions on $\mathbb{S}^2,$ the unit sphere embedded in $\mathbb{R}^3$. The construct of these kernels utilizes the Legendre…