Related papers: Metric duality between positive definite kernels a…
Let "mu" be a point process on a countable discrete space "X". Under assumption that "mu" is quasi-invariant with respect to any finitary permutation of "X", we describe a general scheme for constructing an equilibrium Kawasaki dynamics for…
We consider linear approximation based on function evaluations in reproducing kernel Hilbert spaces of certain analytic weighted power series kernels and stationary kernels on the interval $[-1,1]$. Both classes contain the popular Gaussian…
We study integration and $L^2$-approximation in the worst-case setting for deterministic linear algorithms based on function evaluations. The underlying function space is a reproducing kernel Hilbert space with a Gaussian kernel of tensor…
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…
The purpose of this article is threefold: Firstly, we propose some enhancements to the existing definition of 6-functor formalisms. Secondly, we systematically study the category of kernels, which is a certain 2-category attached to every…
Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
This article examines Gaussian processes generated by monotonically modulating stationary kernels. An explicit isometry between the original and the modulated reproducing kernel Hilbert spaces is established, preserving eigenvalues and…
We present a formal verification of the functional correctness of the Muen Separation Kernel. Muen is representative of the class of modern separation kernels that leverage hardware virtualization support, and are generative in nature in…
Hilbert-Schmidt independence criterion and distance covariance are methods to describe independence of random variables using either the Kronecker product of positive definite kernels or the Kronecker product of conditionally negative…
Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the…
We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole domain of positive-definiteness. This…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This…
The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that…
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying…
A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple…