We continue our recent study on constructing a refinement kernel for a given kernel so that the reproducing kernel Hilbert space associated with the refinement kernel contains that with the original kernel as a subspace. To motivate this study, we first develop a refinement kernel method for learning, which gives an efficient algorithm for updating a learning predictor. Several characterization...

The theory of reproducing kernel Hilbert spaces (RKHSs) has been developed into a powerful tool in mathematics and lots applications many fields, especially machine learning. Fractal provides new technologies for making complicated curves fitting experimental data. Recently, combinations fractal interpolation functions (FIFs) methods curve estimations have attracted the attention researchers. W...

Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular successful machine learning techniques. From mathematical point of view, these methods rest on concept kernels function spaces generated kernels, so–called reproducing kernel Hilbert spaces. Motivated recent developments approaches in context interacting particle systems, ...

The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from numerical analysis standpoint. basic problem of finding an algorithm for efficient integration functions reproduced by kernels not been fully solved. In this article we construct two classes algorithms that use <inline-formu...

Reinforcement learning consists of finding policies that maximize an expected cumulative long-term reward in a Markov decision process with unknown transition probabilities and instantaneous rewards. In this article, we consider the problem such optimal while assuming they are continuous functions belonging to reproducing kernel Hilbert space (RKHS). To learn policy, introduce stochastic policy...

We give several properties of the reproducing kernel Hilbert spaces induced by the Gaussian kernel and their implications for recent results in the complexity of the regularized least square algorithm in learning theory.

Kernel Fisher’s linear discriminant analysis (KFLDA) has been proposed for nonlinear binary classification (Mika, Rätsch, Weston, Schölkopf and Müller, 1999, Baudat and Anouar, 2000). It is a hybrid method of the classical Fisher’s linear discriminant analysis and a kernel machine. Experimental results (e.g., Schölkopf and Smola, 2002) have shown that the KFLDA performs slightly better in terms...