Statistical Mechanics of Soft Margin Classifiers

Details Statistical Mechanics of Soft Margin Classifiers Statistical Mechanics of Soft Margin Classifiers

2001-02-18

arxiv.org/abs/cond-mat/0102319v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

26 pages, 12 figures, submitted to Physical Review E

Scientific paper

10.1103/PhysRevE.64.031907

We study the typical learning properties of the recently introduced Soft Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of Statistical Mechanics. We derive analytically the behaviour of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the generalization error towards the asymptotic value, depending on the task and on general characteristics of the distribution of stabilities of the patterns to be learned. The optimal learning curves of the SMCs, which give the minimal generalization error, are obtained by tuning the coefficient controlling the trade-off between the error and the regularization terms in the cost function. If the task is realizable by the SMC, the optimal performance is better than that of a hard margin Support Vector Machine and is very close to that of a Bayesian classifier.

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