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|Title: ||Learning with kernel based regularization schemes|
|Other Titles: ||Ji yu he de zheng ze hua xue xi suan fa|
|Authors: ||Xiao, Quanwu (肖銓武)|
|Department: ||Department of Mathematics|
|Degree: ||Doctor of Philosophy|
|Issue Date: ||2009|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Machine learning.|
|Notes: ||CityU Call Number: Q325.5 .X53 2009|
v, 81 leaves 30 cm.
Thesis (Ph.D.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves -81)
|Abstract: ||Learning theory is the mathematical foundation for machine learning algorithms
which have important applications in many areas of science and technology. In
this thesis, we mainly consider learning algorithms involving kernel based regularization
schemes. While algorithms like support vector machine given by Tikhonov
regularization schemes associated with convex loss functions and reproducing kernel
Hilbert spaces have been extensively studied in the literature, we introduce
some non-standard settings and provide insightful analysis for them.
Firstly, we study a regression algorithm with `1 regularizer stated in a hypothesis
space trained from data or samples by a nonsymmetric kernel. The data
dependent nature of the algorithm leads to an extra error term called hypothesis
error, which is essentially different from regularization schemes with data independent
hypothesis spaces. By dealing with regularization error, sample error
and hypothesis error, we estimate the total error in terms of properties of the
kernel, the input space, the marginal distribution, and the regression function of
the regression problem. Learning rates are derived by choosing suitable values of
the regularization parameter. An improved error decomposition approach is used
in our data dependent setting.
Secondly, we consider the binary classification problem by learning from samples
drawn from a non-identical sequence of probability measures. Our main goal
is to provide satisfactory estimates for the excess misclassification error of the
produced classifiers. Similar results can be obtained for multi-class classification
because we give a comparison theory for error analysis of multi-class classifiers.
Finally, we consider the sparsity issue for `1 regularization schemes. This topic has attracted a lot of attention recently and we give some discussion for
further study on both theoretical and practical aspects.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b3008236|
|Appears in Collections:||MA - Doctor of Philosophy |
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