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Research interests
My most recent interests are focusing on mathematics for data sciences, in particular topological and geometric methods for high dimensional data analysis and statistical machine learning, with applications in computational biology and information technology.
Monograph
A Dynamic Theory of Learning. PhD Dissertation, University of Calfornia at Berkeley. Supervisor: Steve Smale. December, 2006.
Published as A Dynamic Theory of Learning -- Online Learning and Stochastic Algorithms in Reproducing Kernel Hilbert Spaces, Verlag Dr. Muller, ISBN: 978-3-639-09390-2. 2008.
A Mathematical Introduction to Data Analysis. preprint.
Papers and Preprints