Related papers: Gaussian RBF-kernels via Fock spaces: quaternionic…
The Gaussian kernel and its derivatives have already been employed for Convolutional Neural Networks in several previous works. Most of these papers proposed to compute filters by linearly combining one or several bases of fixed or slightly…
The aim of this article is to establish two-sided Gaussian bounds for the heat kernels on the unit ball and simplex in $\mathbb{R}^n$, and in particular on the interval, generated by classical differential operators whose eigenfunctions are…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
The notion of the eigenvalue problem in the Fock space with polynomial eigenfunctions is introduced. This problem is classified by using the finite-dimensional representations of the $\mathfrak{sl}(2)$-algebra in Fock space. In the complex…
We prove that Centered Kernel Alignment (CKA) based on a Gaussian RBF kernel converges to linear CKA in the large-bandwidth limit. We show that convergence onset is sensitive to the geometry of the feature representations, and that…
Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to…
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…
Bayesian optimization with Gaussian processes (GP) is commonly used to optimize black-box functions. The Mat\'ern and the Radial Basis Function (RBF) covariance functions are used frequently, but they do not make any assumptions about the…
Quadrature formulas (QFs) based on radial basis functions (RBFs) have become an essential tool for multivariate numerical integration of scattered data. Although numerous works have been published on RBF-QFs, their stability theory can…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…
Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation…
Complex-valued neural networks (CVNNs) have been shown to be powerful nonlinear approximators when the input data can be properly modeled in the complex domain. One of the major challenges in scaling up CVNNs in practice is the design of…
Exploiting symmetry in Groebner basis computations is difficult when the symmetry takes the form of a group acting by automorphisms on monomials in finitely many variables. This is largely due to the fact that the group elements, being…
In this paper we study mixed norm boundedness for fractional integrals related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. The key point is the analysis of weighted inequalities for fractional integral…
In this paper, we study a specific system of Clifford-Appell polynomials and in particular their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions.…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
The introduction of operator states and of observables in various fields of quantum physics has raised questions about the mathematical structures of the corresponding spaces. In the framework of third quantization it had been conjectured…
In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…
We will present an algebra describing a mixed paraparticle model, known in the bibliography as "The Relative Parabose Set (\textsc{Rpbs})". Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom…
Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…