JSM 2011 Online Program

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Abstract Details

Activity Number: 410
Type: Contributed
Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301312
Title: Radial Basis Function Regularization for Linear Inverse Problems with Random Noise
Author(s): Carlos Valencia*+ and Ming Yuan
Companies: Georgia Institute of Technology and Georgia Institute of Technology
Address: 1017 North Ave NE, Atlanta, GA, 30306-4414, US
Keywords: Inverse problems ; minimax ; regularization ; radial basis function
Abstract:

In this paper, we study the statistical properties of method of regularization with radial basis functions in the context of linear inverse problems. Radial basis function regularization is widely used in machine learning because of its demonstrated effectiveness in numerous applications and computational advantages. From a statistical viewpoint, one of the main advantages of radial basis function regularization in general and Gaussian radial basis function regularization in particular is their ability to adapt to varying degree of smoothness in a direct problem. We show here that similar approaches for inverse problems not only share such adaptivity to the smoothness of the signal but also can accommodate different degrees of ill-posedness. These results render further theoretical support to the superior performance observed empirically for radial basis function regularization.


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