TR announcement

[Ralf Herbrich]

We would like to announce the availability of the following technical report

	Bayesian Learning in Reproducing Kernel Hilbert Spaces
	Ralf Herbrich, Thore Graepel, Colin Campbell

Abstract

Support Vector Machines find the hypothesis that corresponds to the centre
of the largest hypersphere that can be placed inside version space, i.e.
the space of all consistent hypotheses given a training set. The
boundaries of version space touched by this hypersphere define the support
vectors. An even more promising approach is to construct the hypothesis
using the whole of version space. This is achieved by the Bayes point: the
midpoint of the region of intersection of all hyperplanes bisecting
version space into two volumes of equal magnitude. It is known that the
centre of mass of version space approximates the Bayes point. The centre
of mass is estimated by averaging over the trajectory of a billiard in
version space. We derive bounds on the generalisation error of Bayesian
classifiers in terms of the volume ratio of version space and parameter
space. This ratio serves as an effective VC dimension and greatly
influences generalisation. We present experimental results indicating that
Bayes Point Machines consistently outperform Support Vector Machines.
Moreover, we show theoretically and experimentally how Bayes Point
Machines can easily be extended to admit training errors. 


The gziped PS file can be downloaded at

	http://stat.cs.tu-berlin.de/~ralfh/bayes.ps.gz



Best regards

Ralf Herbrich, Thore Graepel, and Colin Campbell

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 Ralf Herbrich	        phone : +49-30-314-25817
 TU Berlin              email : ralfh at cs.tu-berlin.de
 FB 13; FR 6-9          URL   : http://stat.cs.tu-berlin.de/~ralfh
 10587 Berlin                    
 Germany

   [teaching assistant in the statistics group at the TU Berlin]
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