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|Title: ||Learning with trigonometric polynomials|
|Other Titles: ||Ji yu san jiao duo xiang shi de xue xi|
|Authors: ||Zhao, Yulong (赵玉龙)|
|Department: ||Department of Mathematics|
|Degree: ||Master of Philosophy|
|Issue Date: ||2009|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Machine learning.|
|Notes: ||CityU Call Number: Q325.5 .Z45 2009|
v, 41 leaves 30 cm.
Thesis (M.Phil.)--City University of Hong Kong, 2009.
Includes bibliographical references (leaves 38-41)
|Abstract: ||In this thesis, we will focus on two problems in learning theory.
Firstly, we will discuss the problem of reconstruction of multivariable
trigonometric polynomials. This is a special example of learning in finite
dimensional spaces. To estimate the constant number of least square
algorithm, we derive an inequality for the Hilbert-Schmidt norm of the
difference between the sample second moment matrix m-1ULU and its
expectation by a probability inequality of Hilbert space valued variables
where U is a complex random m x D matrix with independent rows.
This result immediately implies a bound on condition number of the
sample second moment matrix. The results provide a solid theoretical
foundation for those efficient numerical algorithms. A relaxed condition
was used to generalize the result about trigonometric polynomials.
Secondly, we will consider computing the empirical task function of regularity
problems. This could be considered as an extension of the results
of learning with trigonometric polynomials in our points of view. We
will give a bound about the condition number of the regularity algorithm.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2375047|
|Appears in Collections:||MA - Master of Philosophy |
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