NewTR: SVM's-RKHS-GACV

[Grace Wahba]

`Support Vector Machines, Reproducing Kernel Hilbert 
Spaces and the Randomized GACV', University of 
Wisconsin-Madison Statistics Department TR 984, Nov 1997
by Grace Wahba available at 

URL ftp://ftp.stat.wisc.edu/pub/wahba/nips97.ps.gz

or via my home page http://www.stat.wisc.edu/~wahba -> TRLIST 

...........Abstract............................
This report is intended as background 
material for a talk to be presented in the 
NIPS 97 Workshop on Support Vector Machines (SVM's).
It consists of three parts: (1) A brief review 
of some old but relevant results on constrained optimization 
in Reproducing Kernel Hilbert Spaces (RKHS); 
and a review of the relationship 
between zero-mean Gaussian processes
and RKHS. Application of tensor sums and products of 
RKHS including smoothing spline ANOVA spaces
in the context of SVM's also described.
(2) Discussion of the relationship between
penalized likelihood methods in RKHS for Bernoulli 
data when the goal is risk factor estimation, and 
SVM methods in RKHS when the goal is classification. When the 
goal is classification it is noted 
replacing the likelihood 
functional of the logit [log odds ratio]
with an appropriate  SVM functional is a 
natural method for 
concentrating computational effort 
on estimating the logit near the classification 
boundary and ignoring data far away. 
Remarks concerning the potential of 
SVM's for variable selection
as an efficient preprocessor for risk factor 
estimation are made.
(3) A discussion of how the the GACV 
for choosing smoothing parameters proposed
in Xiang and Wahba (1996, 1997) may be implemented
in the context of convex SVM's.