NIPS 97 Workshop on Support Vector Machines
NIPS 97 Workshop on Support Vector Machines
Title: Reproducing Kernel Hilbert Spaces,
Smoothing Spline ANOVA Spaces, Support Vector
Machines, and all that.
Talk by
Grace Wahba
at the NIPS Support Vector Learning Machines Workshop,
December 6, 1997, at Breckenridge CO. Think snow.
Abstract:
In this (mostly) review talk,
We look at reproducing kernel Hilbert spaces (rkhs)
as a natural home for studying
certain support vector machines and their relations with
other multivariate function estimation paradigms.
We examine Lemma 6.1 of Kimeldorf and Wahba (J. Math.
Anal. Applic. 1971, p 92) concerning linear inequality
constraints in rkhs, and note how it applies
in arbitrary rkhs. We will particularly note
the potential use of the reproducing kernels
(rk's) associated with smoothing spline ANOVA spaces,
for applications with heterogenous predictor
variables, and possibly as a tool in variable
selection as well as exemplar selection.
Questions about the possible internal
`tuning' of SVM's (as compared to the use
of test sets) and the `degrees of freedom
for signal' will be raised, although probably
not answered.
Key words:
support vector machines,
reproducing kernel Hilbert spaces,
penalized likelihood,
smoothing spline ANOVA,
radial basis functions,
Gaussian processes and Bayes estimates,
sigmoidal basis functions,
greedy algorithms,
regularization,
generalized cross validation,
generalized approximate cross validation
Click here
for G. Wahba, Support Vector Machines, Reproducing Kernel Hilbert
Spaces and the Randomized GACV, University of Wisconsin-Madison
Statistics Department TR 984rr. Revised basis for
part of my SVM Workshop talk.
typos
Click here
for Grace Wahba, Students and Colleagues
recent Technical Reports.
The home page
for the Support Vector Learning Machines Workshop is
here.
Here
is an announcement for `Advances in Kernel Methods
Support Vector Learning' a book based on the conference
talks.
Click here
for Grace Wahba's publications.