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

A family of regularized least squares regression models in a Reproducing Kernel Hilbert Space is extended by the kernel partial least squares (PLS) regression model. Similar to principal components regression (PCR), PLS is a method based on the projection of input (explanatory) variables to the latent variables (components). However, in contrast to PCR, PLS creates the components by modeling th...

A framework for coherent pattern extraction and prediction of observables measure-preserving, ergodic dynamical systems with both atomic continuous spectral components is developed. This based on an approximation the generator system by a compact operator Wτ reproducing kernel Hilbert space (RKHS). The skew-adjoint, thus can be represented projection-valued measure, discrete compactness, associ...

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.

and Applied Analysis 3 2. Several Reproducing Kernel Spaces In this section, several reproducing kernels needed are constructed in order to solve 1.1 and 1.2 using RKHSmethod. Before the construction, we utilize the reproducing kernel concept. Throughout this paper C is the set of complex numbers, L2 a, b {u | ∫b a u2 x dx < ∞}, l2 {A | ∑∞i 1 Ai 2 < ∞}, and the superscript n in u n t denotes th...

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...