Doctor of Philosophy, The Ohio State University, 2016, Computer Science and Engineering
Supervised learning algorithms have achieved significant success in the last decade. To further improve learning performance, we still need to have a better understanding of semi-supervised learning algorithms for leveraging a large amount of unlabeled data. In this dissertation, a new approach for semi-supervised learning will be discussed, which takes advantage of unlabeled data information through an integral operator associated with a kernel function. More specifically, several problems in machine learning are formulated as a regularized Fredholm integral equation, which has been well studied in the literature of inverse problems. Under this framework, we propose several simple and easily implementable algorithms with sound theoretical guarantees.
First, a new framework for supervised learning is proposed, referred as Fredholm learning. It allows a natural way to incorporate unlabeled data and is flexible on the choice of regularizations. In particular, we connect this new learning framework to the classical algorithm of radial basis function networks, and more specifically, analyze two common forms of regularization procedures for RBF networks, one based on the square norm of coefficients in a network and another one using centers obtained by the k-means clustering. We provide a theoretical analysis of these methods as well as a number of experimental results, pointing out very competitive empirical performance as well as certain advantages over the standard kernel methods in terms of both flexibility (incorporating unlabeled data) and computational complexity. Moreover, the Fredholm learning algorithm could be interpreted as a special form of kernel methods using a data-dependent kernel. Our analysis shows that Fredholm kernels achieve noise suppressing effects under a new assumption for semi-supervised learning, termed the "noise assumption".
We also address the problem of estimating the probability density ratio function q/p, which could be used for s (open full item for complete abstract)
Committee: Mikhail Belkin (Advisor); Wang Yusu (Committee Member); Wang DeLiang (Committee Member); Lee Yoonkyung (Committee Member)
Subjects: Computer Science