Given a positive definite, bounded linear operator A on the Hilbert space H0 := l(E), we consider a reproducing kernel Hilbert space H+ with a reproducing kernel A(x, y). Here E is any countable set and A(x, y), x, y ∈ E, is the representation of A w.r.t. the usual basis of H0. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space H − with a ke...

We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.

This paper presents a novel learning scenario which combines dimensionality reduction, supervised learning as well as kernel selection. We carefully define the hypothesis class that addresses this setting and provide an analysis of its Rademacher complexity and thereby provide generalization guarantees. The proposed algorithm uses KPCA to reduce the dimensionality of the feature space, i.e. by ...

In this paper we discuss about nonlinear pseudoparabolic equations with nonlocal boundary conditions and their results. An effective error estimation for this method altough has not yet been discussed. The aim of this paper is to fill this gap.

We propose a fully Bayesian methodology for generalized kernel mixed models (GKMMs), which are extensions of generalized linear mixed models in the feature space induced by a reproducing kernel. We place a mixture of a point-mass distribution and Silverman’s g-prior on the regression vector of a generalized kernel model (GKM). This mixture prior allows a fraction of the components of the regres...

It is a well known fact that transfer functions of scattering conservative systems and impedance conservative system are the analytic contractive function in the unit disk and functions with positive real part on the upper half plane, respectively. In this case, the interplay between the transfer functions is via the Moebius transformation. In the system representation the interplay is by the s...

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). The embedding function has been proven to be injective when the reproducing kernel is universal. In this...

We focus on covariance criteria for finding a suitable subspace for regression in a reproducing kernel Hilbert space: kernel principal component analysis, kernel partial least squares and kernel canonical correlation analysis, and we demonstrate how this fits within a more general context of subspace regression. For the kernel partial least squares case some variants are considered and the meth...

In this paper we introduce a generalization of the classical L2(R)-based Sobolev spaces with the help of a vector differential operator P which consists of finitely or countably many differential operators Pn which themselves are linear combinations of distributional derivatives. We find that certain proper full-space Green functions G with respect to L = P∗TP are positive definite functions. H...