Abstract

A number of results have bounded generalization of a classifier in terms of its margin on the training points. There has been some debate about whether the minimum margin is the best measure of the distribution of training set margin values with which to estimate the generalization. Freund and Schapire [7] have shown how a different function of the margin distribution can be used to bound the number of mistakes of an on-line learning algorithm for a perceptron, as well as an expected error bound. ShaweTaylor and Cristianini [13] showed that a slight generalization of their construction can be used to give a pac style bound on the tail of the distribution of the generalization errors that arise from a given sample size. We show that in the linear case the approach can be viewed as a change of kernel and that the algorithms arising from the approach are exactly those originally proposed by Cortes and Vapnik [4]. We generalise the basic result to function classes with bounded fat-shatteri...

Citations