2003 | OriginalPaper | Buchkapitel
Simplified PAC-Bayesian Margin Bounds
verfasst von : David McAllester
Erschienen in: Learning Theory and Kernel Machines
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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The theoretical understanding of support vector machines is largely based on margin bounds for linear classifiers with unit-norm weight vectors and unit-norm feature vectors. Unit-norm margin bounds have been proved previously using fat-shattering arguments and Rademacher complexity. Recently Langford and Shawe-Taylor proved a dimension-independent unit-norm margin bound using a relatively simple PAC-Bayesian argument. Unfortunately, the Langford-Shawe-Taylor bound is stated in a variational form making direct comparison to fat-shattering bounds difficult. This paper provides an explicit solution to the variational problem implicit in the Langford-Shawe-Taylor bound and shows that the PAC-Bayesian margin bounds are significantly tighter. Because a PAC-Bayesian bound is derived from a particular prior distribution over hypotheses, a PAC-Bayesian margin bound also seems to provide insight into the nature of the learning bias underlying the bound.