Kernels and geometry of machine learning

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Title Kernels and geometry of machine learning
Publication Type dissertation
School or College College of Engineering
Department Computing
Author Moeller, John
Date 2017
Description The contributions in the area of kernelized learning techniques have expanded beyond a few basic kernel functions to general kernel functions that could be learned along with the rest of a statistical learning model. This dissertation aims to explore various directions in \emph{kernel learning}, a setting where we can learn not only a model, but also glean information about the geometry of the data from which we learn, by learning a positive definite (p.d.) kernel. Throughout, we can exploit several properties of kernels that relate to their \emph{geometry} -- a facet that is often overlooked. We revisit some of the necessary mathematical background required to understand kernel learning in context, such as reproducing kernel Hilbert spaces (RKHSs), the reproducing property, the representer theorem, etc. We then cover kernelized learning with support vector machines (SVMs), multiple kernel learning (MKL), and localized kernel learning (LKL). We move on to Bochner's theorem, a tool vital to one of the kernel learning areas we explore. The main portion of the thesis is divided into two parts: (1) kernel learning with SVMs, a.k.a. MKL, and (2) learning based on Bochner's theorem. In the first part, we present efficient, accurate, and scalable algorithms based on the SVM, one that exploits multiplicative weight updates (MWU), and another that exploits local geometry. In the second part, we use Bochner's theorem to incorporate a kernel into a neural network and discover that kernel learning in this fashion, continuous kernel learning (CKL), is superior even to MKL.
Type Text
Publisher University of Utah
Subject Kernel Learning; Machine Learning; Multiple Kernel Learning; Support Vector Machines
Dissertation Name Doctor of Philosophy
Language eng
Rights Management ©John Moeller
Format application/pdf
Format Medium application/pdf
ARK ark:/87278/s61p25dx
Setname ir_etd
ID 1345352
Reference URL https://collections.lib.utah.edu/ark:/87278/s61p25dx
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