Abstract
In this paper, we study the statistical properties of the 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 degrees 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.