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Nonlinear Knowledge in Kernel Approximation

Professor Olvi Mangasarian
UCSD Department of Mathematics


Prior knowledge over arbitrary general sets is incorporated intononlinear kernel approximation problems in the form of linearconstraints in a linear program. The key tool in this incorporation isa theorem of the alternative for convex functions that convertsnonlinear prior knowledge implications into linear inequalitieswithout the need to kernelize these implications. Effectiveness of theproposed formulation is demonstrated on two synthetic examples and animportant lymph node metastasis prediction problem. All these problemsexhibit marked improvements upon the introduction of prior knowledgeover nonlinear kernel approximation approaches that do not utilizesuch knowledge. (Joint work with my PhD student Edward (Ted) W. Wild)

Tuesday, January 24, 2006
11:00AM AP&M 2402