Frames, Reproducing Kernels, Regularization and Learning

Reproducing kernels and regularization methods in machine learning

Learnability of Gaussians with Flexible Variances

Gaussian kernels with flexible variances provide a rich family of Mercer kernels for learning algorithms. We show that the union of the unit balls of reproducing kernel Hilbert spaces generated by Gaussian kernels with flexible variances is a uniform Glivenko-Cantelli (uGC) class. This result confirms a conjecture concerning learnability of Gaussian kernels and verifies the uniform convergence ...

Kernels for Multi--task Learning

This paper provides a foundation for multi–task learning using reproducing kernel Hilbert spaces of vector–valued functions. In this setting, the kernel is a matrix–valued function. Some explicit examples will be described which go beyond our earlier results in [7]. In particular, we characterize classes of matrix– valued kernels which are linear and are of the dot product or the translation in...

Adaptive Kernel Based Machine Learning Methods

During the support period July 1, 2011 June 30, 2012, seven research papers were published. They consist of three types: • Research that directly addresses the kernel selection problem in machine learning [1, 2]. • Research that closely relates to the fundamental issues of the proposed research of this grant [3, 4, 5, 6]. • Research that is in the general context of computational mathematics [7...

Logic, Trees and Kernels

Kernel based methods achieved much of their initial success on problems with real valued attributes. There are many problems with discrete attributes (including Boolean) and in this paper we present a number of results concerning the kernelisation of Boolean and discrete problems. We give results about the learnability and required complexity of logical formulae to solve classification problems...