Related papers: Universal kernels via harmonic analysis on Riemann…

We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

We present a characterization for a positive definite operator valued kernel to be universal or $C_{0}$-universal, and apply these characterizations to a family of operator valued kernels that are shown to be well behaved. Later, we obtain…

We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in ${\Bbb C}^d$ for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus 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…

We prove two new equivalences of the Feichtinger conjecture that involve reproducing kernel Hilbert spaces. We prove that if for every Hilbert space, contractively contained in the Hardy space, each Bessel sequence of normalized kernel…

Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In…

We use heat kernels or eigenfunctions of the Laplacian to construct local coordinates on large classes of Euclidean domains and Riemannian manifolds (not necessarily smooth, e.g. with $\mathcal{C}^\alpha$ metric). These coordinates are…

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…

This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…

Suppose H is a space of functions on X. If H is a Hilbert space with reproducing kernel then that structure of H can be used to build distance functions on X. We describe some of those and their interpretations and interrelations. We also…

Over the last decade several positive definite kernels have been proposed to treat spike trains as objects in Hilbert space. However, for the most part, such attempts still remain a mere curiosity for both computational neuroscientists and…

The classical Newtonian potentials, defined in terms of metrics, give rise to the basic family of kernels defining linear integral operators and posing the fundamental problems of linear harmonic analysis. When the binary character of a…

We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their…

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…

$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…

Mercer's expansion and Mercer's theorem are cornerstone results in kernel theory. While the classical Mercer's theorem only considers continuous symmetric positive definite kernels, analogous expansions are effective in practice for…

Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…

Feature maps associated with positive definite kernels play a central role in kernel methods and learning theory, where regularity properties such as Lipschitz continuity are closely related to robustness and stability guarantees. Despite…