  We show that the multi-class support vector machine (MSVM) proposed by Lee
et. al. (2004), can be viewed as a MAP estimation procedure under an
appropriate probabilistic interpretation of the classifier. We also show that
this interpretation can be extended to a hierarchical Bayesian architecture and
to a fully-Bayesian inference procedure for multi-class classification based on
data augmentation. We present empirical results that show that the advantages
of the Bayesian formalism are obtained without a loss in classification
accuracy.
