the theory of infinitely divisible positive definite functions. Fundamentals of this theory and the theory of reproducing kernel Hilbert spaces are reviewed and applied in establishing the validity of the method.

use of these methods in an online setting suitable for real-time applications. In this paper we consider online learning in a Reproducing Kernel Hilbert Space. By considering classical stochastic gradient descent within a feature space, and the use of some straightforward tricks, we develop simple

We present a class of algorithms for independent component analysis (ICA) which use contrast functions based on canonical correlations in a reproducing kernel Hilbert space. On the one hand, we show that our contrast functions are related to mutual information and have desirable mathematical

algorithms and standard methods including Support Vector Machines and Regularized Least Squares can be obtained as special cases. We utilize properties of Reproducing Kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely

Abstract—This paper provides a functional analysis perspective of information-theoretic learning (ITL) by defining bottom-up a reproducing kernel Hilbert space (RKHS) uniquely determined by the symmetric nonnegative definite kernel function known as the cross-information potential (CIP). The CIP

this paper we very briefly review some of these results. RKHS can be chosen tailored to the problem at hand in many ways, and we review a few of them, including radial basis function and smoothing spline ANOVA spaces. Girosi (1997), Smola and Scholkopf (1997), Scholkopf et al (1997) and others have

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

using covariance operators on reproducing kernel Hilbert spaces. This characterization allows us to derive a contrast function for estimation of the effective subspace. Unlike many conventional methods for dimensionality reduction in supervised learning, the proposed method requires neither assumptions

We reformulate the original component-by-component algorithm for rank-1 lattices in a matrix-vector notation so as to highlight its structural properties. For function spaces similar to a weighted Korobov space, we derive a technique which has construction cost O(sn log(n)), in contrast

and pleasure to work under his guidance. I just hope that some day I can be as good a mathematician as him. Next, I would like to thank my thesis committee members, Dr. David P. Blecher, Dr. Bernhard G. Bodmann, and Dr. David Sherman, for careful reading of my thesis, helpful suggestions, and ideas for future