[ugrads] Invitation for the Comprehensive Exam for Xuan Zhou

Myrna Walker mwalke13 at iit.edu
Fri Mar 28 11:31:28 CDT 2014


Dear All,



Please join the Xuan Zhou for his comprehensive exam.



When: Wednesday, April 2, 2014, 10:00 am

Where: Stuart Building - Room 223


Title: TRACTABILITY OF FUNCTION APPROXIMATION PROBLEMS WITH GENERAL KERNELS

Abstract: This talk addresses the problem of approximating functions
belonging to a reproducing kernel Hilbert space. Often convergence rates
deteriorate quickly as the dimension of problem increases. Such a behavior
is known as the curse of dimensionality. Therefore it is desirable to have
dimension independent convergence rates, which corresponds to the concept
of strong polynomial tractability. Such tractability results have been
established for anisotropic Gaussian reproducing kernels.



We study the conditions for tractability on more general kernels of product
form. The shape parameter, gamma, governs the horizontal scale of a
function with respect to different input variables. We also introduce a
parameter, alpha, which governs the vertical scale of the function with
respect to different variables. The exponent of strong tractability depends
on how quickly the sequence (alpha*gamma) tends to zero.


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