From Margin to Sparsity

Part of Advances in Neural Information Processing Systems 13 (NIPS 2000)

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Thore Graepel, Ralf Herbrich, Robert C. Williamson


We present an improvement of Novikoff's perceptron convergence theorem. Reinterpreting this mistake bound as a margin dependent sparsity guarantee allows us to give a PAC-style generalisation er(cid:173) ror bound for the classifier learned by the perceptron learning algo(cid:173) rithm. The bound value crucially depends on the margin a support vector machine would achieve on the same data set using the same kernel. Ironically, the bound yields better guarantees than are cur(cid:173) rently available for the support vector solution itself.