R. Dietrich and M. Opper (2000)
Support Vectors and Statistical Mechanics
In: Advances in Large Margin Classifiers, ed. by A.J. Smola and P.L. Bartlett and B. Schölkopf and D. Schuurmans, pp. 359-368, Cambridge, MA, MIT Press.
SVMs are analyzed using methods of statistical mechanics by representing the SVM solution as the limit of a family of Gibbs distributions. This way, one may derive rather precise learning curves. The analysis in the paper shows that for `favourable' input distributions, i.e. ones which allow a large margin, the expected generalization error decays much more rapidly than predicted by distribution-independent upper bounds of statistical learning theory.