A Variety of Regularization problems


      Grace Wahba
      Univ of Wisconsin
      Statistics


            Abstract

We review a selected class of regularization problems which 
balance distance to the observations with a penalty 
on the complexity or size of the solution. 
Considered are a variety of definitions of 'closeness', 
and several selected penalties, based on RKHS or $l_1$ norms.
A class of tuning methods which generalize the 
Generalized Cross Validation (GCV) to 
distance criteria other than least squares are noted. 
Smoothing Spline ANOVA (SS-ANOVA) models will 
be described, and their use in a study selecting important
important variables affecting the risk of progression 
of an eye disease, based on data from a demographic 
study. 
Variable/Model selection will be based on the Likelihood 
Basis Pursuit method described in  Zhang et al, 
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