Related papers: Reproducing Kernel Functions: A general framework …

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…

We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled…

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…

Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

We study two extension problems, and their interconnections: (i) extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; and (ii) (in case of Lie groups $G$) representations of the…

By selecting different filter functions, spectral algorithms can generate various regularization methods to solve statistical inverse problems within the learning-from-samples framework. This paper combines distributed spectral algorithms…

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…

Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces where all the evaluation functionals are linear and bounded. They are in one-to-one correspondence with positive definite maps called kernels. Stable RKHSs enjoy the…

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…

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…

We study post-training interpretability for Support Vector Machines (SVMs) built from truncated orthogonal polynomial kernels. Since the associated reproducing kernel Hilbert space is finite-dimensional and admits an explicit tensor-product…

Usually, complex-valued RKHS are presented as an straightforward application of the real-valued case. In this paper we prove that this procedure yields a limited solution for regression. We show that another kernel, here denoted as pseudo…

A central challenge in reinforcement learning (RL) is to learn models that generalize beyond the tasks on which they are trained, a goal traditionally pursued through multi-task and meta RL. Recently, transformer architectures have emerged…

In this paper, we have considered vector valued reproducing kernel Hilbert spaces (RKHS) $\mathcal{H}$ of entire functions associated with operator valued kernel functions. de Branges operators $\mathfrak{E}=(E_- , E_+)$ analogous to de…

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…

Differentiable rendering is a technique that aims to invert the rendering process to enable optimizing rendering parameters from a set of images. In this article, we present a differentiable volume rendering solution called DiffTetVR for…

A reproducing kernel Hilbert space (RKHS) has four well-known easily derived properties. Since these properties are usually not emphasized as a simple means of gaining insight into RKHS structure, they are singled out and proved in this…

In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…

Artificial neural networks show promising performance in detecting correlations within data that are associated with specific outcomes. However, the black-box nature of such models can hinder the knowledge advancement in research fields by…