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Title: Learning with centered reproducing kernels
Authors: Wang, Chendi
Advisors: Chen, Xiaojun (AMA)
Guo, Xin (AMA)
Keywords: Kernel functions
Hilbert space
Issue Date: 2018
Publisher: The Hong Kong Polytechnic University
Abstract: In the past twenty years, reproducing kernels and the kernel-based learning algorithms have been widely and successfully applied to many areas of scientific research and industry, and are extensively studied. Many of these algorithms take the form of an optimization problem. Typically, the objective function consists of a fidelity term for fitting the observations, and a regularization term for preventing over-fitting. Examples include the support vector machines for classification, and the regularized least squares for regression. However, in many regression problems, the constant component should be treated differently in the regression function, and the existing kernel methods are not perfect tools to model this difference. Examples include score-based ranking function regression. In this thesis, we study a class of Centered Reproducing Kernels (CRKs), which separate the constant component from the reproducing kernel Hilbert spaces. We provide the non-asymptotic convergence analysis of the empirical CRK-based regularized least squares.
Description: x, 66 pages
PolyU Library Call No.: [THS] LG51 .H577M AMA 2018 Wang
Rights: All rights reserved.
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