This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method,the Gram-Schmidt process is omitted here and satisfactory results are obtained. The analytical solution is represented in the form of series. An iterative method is given to obtain the approximate solution. The conv...

We investigate the construction of all reproducing kernel Hilbert spaces of functions on a domain Ω ⊂ R that have a countable sampling set Λ ⊂ Ω. We also characterize all the reproducing kernel Hilbert spaces that have a prescribed sampling set. Similar problems are considered for reproducing kernel Banach spaces, but now with respect to Λ as a p-sampling set. Unlike the general p-frames, we pr...

We focus on three methods 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 a least squares support vector machine style der...

Modeling policies in reproducing kernel Hilbert space (RKHS) renders policy gradient reinforcement learning algorithms non-parametric. As a result, the policies become very flexible and have a rich representational potential without a predefined set of features. However, their performances might be either non-covariant under reparameterization of the chosen kernel, or very sensitive to step-siz...

To improve the performance of subspace classi er, it is e ective to reduce the dimensionality of the intersections between subspaces. For this purpose, the feature space is mapped implicitly to a high dimensional reproducing kernel Hilbert space and the subspace classi er is applied in this space. As a result of Hiragana recognition experiment, our classi er outperformed the conventional subspa...

An account of sampling in the setting of reproducing kernel spaces is given, the main point of which is to show that the sampling theory of Kluvánek, even though it is very general in some respects, is nevertheless a special case of the reproducing kernel theory. A Dictionary is provided as a handy summary of the essential steps. Starting with the classical formulation, the notion of band-limit...

Data-Driven Optimization Using Reproducing Kernel Hilbert Spaces