The Journal of Machine Learning Research (www.jmlr.org) is pleased to
announce the availability of a new paper in electronic form.
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Bayes Point Machines
Ralf Herbrich, Thore Graepel and Colin Campbell. Journal of Machine Learning
Research 1 (August 2001), pp. 245-279.
Abstract
Kernel-classifiers comprise a powerful class of non-linear decision
functions for binary classification. The support vector machine is an
example of a learning algorithm for kernel classifiers that singles out the
consistent classifier with the largest margin, i.e. minimal real-valued
output on the training sample, within the set of consistent hypotheses, the
so-called version space. We suggest the Bayes point machine as a
well-founded improvement which approximates the Bayes-optimal decision by
the centre of mass of version space. We present two algorithms to
stochastically approximate the centre of mass of version space: a billiard
sampling algorithm and a sampling algorithm based on the well known
perceptron algorithm. It is shown how both algorithms can be extended to
allow for soft-boundaries in order to admit training errors. Experimentally,
we find that - for the zero training error case - Bayes point machines
consistently outperform support vector machines on both surrogate data and
real-world benchmark data sets. In the soft-boundary/soft-margin case, the
improvement over support vector machines is shown to be reduced. Finally, we
demonstrate that the real-valued output of single Bayes points on novel test
points is a valid confidence measure and leads to a steady decrease in
generalisation error when used as a rejection criterion.
This paper and earlier papers in Volume 1 are available electronically at
http://www.jmlr.org in PostScript, PDF and HTML formats; a bound, hardcopy
edition of Volume 1 will be available later this year.
- -David Cohn, <david.cohn@acm.org>
Managing Editor, Journal of Machine Learning Research
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