Related papers: A Kernel for Hierarchical Parameter Spaces

A class of negative definite kernels is defined in terms of measure spaces. Using this concept, property (T) for a countable group $\G$ is characterized in terms of measure preserving actions of $\G$, as follows. If a set $S$ is translated…

In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.

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…

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…

We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels, i.e. localities which are (in a particular way) extensions of groups by localities. As an application of these…

We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result…

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…

We study representations of positive definite kernels $K$ in a general setting, but with view to applications to harmonic analysis, to metric geometry, and to realizations of certain stochastic processes. Our initial results are stated for…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However,…

Kernels are often developed and used as implicit mapping functions that show impressive predictive power due to their high-dimensional feature space representations. In this study, we gradually construct a series of simple feature maps that…

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…

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…

Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…

We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…

The aim of the paper is to give a full characterization of functions f from I into the real line R (where I is an interval in R that satisfies certain natural conditions) such that for any I-valued positive definite kernel K defined on an…

Graph kernels methods are based on an implicit embedding of graphs within a vector space of large dimension. This implicit embedding allows to apply to graphs methods which where until recently solely reserved to numerical data. Within the…

We study a reproducing kernel Hilbert space of functions defined on the positive integers and associated to the binomial coefficients. We introduce two transforms, which allow us to develop a related harmonic analysis in this Hilbert space.…