Robust Bayes Point Machines
Support V ectorMachines choose the hypothesis corresponding to the centre of the largest hypersphere that can be inscribed in version space. If version space is elongated or irregularly shaped a potentially superior approach is take into account the whole of version space. We propose to construct the Bayes point whic h is approximated by the centre of mass. Our implementation of a Bayes Point Machine (BPM) uses an ergodic billiard to estimate this point in the k ernel space. We show that BPMs outperform hard margin Support Vector Machines (SVMs) on real world datasets. We introduce a technique that allows the BPM to construct hypotheses with non{zero training error similar to soft margin SVMs with quadratic penelisation of the margin slacks. An experimental study reveals that with decreasing penelisation of training error the improvement of BPMs over SVMs decays, a nding that is explained by geometrical considerations.