Related papers: Vector valued reproducing kernel Hilbert spaces an…
Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that…
We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered…
In the Clifford algebra setting the present study develops three reproducing kernel Hilbert spaces of the Paley-Wiener type, namely the Paley-Wiener spaces, the Hardy spaces on strips, and the Bergman spaces on strips. In particular, we…
For a Reproducing Kernel Hilbert Space on a complex domain we give a formula that describes the Hermitean metrics on the domain which are pull-backs of some metric on the (dual of) the RKHS via the evaluation map. Then we consider the…
In this paper we consider the problem of reconstructing an image that is downsampled in the space of its $SE(2)$ wavelet transform, which is motivated by classical models of simple cells receptive fields and feature preference maps in…
Learning the kernel functions used in kernel methods has been a vastly explored area in machine learning. It is now widely accepted that to obtain 'good' performance, learning a kernel function is the key challenge. In this work we focus on…
Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…
The purpose of this work is to explore the existence and properties of reproducing kernel Hilbert subspaces of $L^2(\C, \, d^2z/\pi)$ based on subsets of complex Hermite polynomials. The resulting coherent states (CS) form a family…
Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…
We consider tractability of integration in reproducing kernel Hilbert spaces which are a tensor product of a Walsh space and a Korobov space. The main result provides necessary and sufficient conditions for weak, polynomial and strong…
Covariate shift occurs prevalently in practice, where the input distributions of the source and target data are substantially different. Despite its practical importance in various learning problems, most of the existing methods only focus…
We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…
We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages…
Despite the increasing importance of stochastic processes on linear networks and graphs, current literature on multivariate (vector-valued) Gaussian random fields on metric graphs is elusive. This paper challenges several aspects related to…
Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…
We consider a class of semidirect products $G = \mathbb{R}^n \rtimes H$, with $H$ a suitably chosen abelian matrix group. The choice of $H$ ensures that there is a wavelet inversion formula, and we are looking for criteria to decide under…
In this paper we discuss some topics related to the general theory of frames. In particular we focus our attention to the existence of different 'reconstruction formulas' for a given vector of a certain Hilbert space and to some refinement…
In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating…