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 here.

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...

Support Vector Machines nd the hypothesis that corresponds to the centre of the largest hypersphere that can be placed inside version space, i.e. the space of all consistent hypotheses given a training set. The boundaries of version space touched by this hypersphere de ne the support vectors. An even more promising approach is to construct the hypothesis using the whole of version space. This i...

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...

This works deals with a method for building Reproducing Kernel Hilbert Space (RKHS) from a Hilbert Space with frame elements having special properties. Conditions on existence and method of construction are given. Then, these RKHS are used within the framework of regularization theory for function approximation. Implications on semiparametric estimation are discussed and a multiscale scheme of ...

By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new Fourier transform in general setting processes. Our results serve unify existing tools from analysis.