Structural risk minimization over data-dependent hierarchies

The paper introduces some generalizations of Vapnik's (1982) method of structural risk minimization (SRM). As well as making explicit some of the details on SRM, it provides a result that allows one to trade off errors on the training sample against improved generalization performance. It then...

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Veröffentlicht in:IEEE transactions on information theory 1998-09, Vol.44 (5), p.1926-1940
Hauptverfasser: Shawe-Taylor, J., Bartlett, P.L., Williamson, R.C., Anthony, M.
Format: Artikel
Sprache:eng
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Zusammenfassung:The paper introduces some generalizations of Vapnik's (1982) method of structural risk minimization (SRM). As well as making explicit some of the details on SRM, it provides a result that allows one to trade off errors on the training sample against improved generalization performance. It then considers the more general case when the hierarchy of classes is chosen in response to the data. A result is presented on the generalization performance of classifiers with a "large margin". This theoretically explains the impressive generalization performance of the maximal margin hyperplane algorithm of Vapnik and co-workers (which is the basis for their support vector machines). The paper concludes with a more general result in terms of "luckiness" functions, which provides a quite general way for exploiting serendipitous simplicity in observed data to obtain better prediction accuracy from small training sets. Four examples are given of such functions, including the Vapnik-Chervonenkis (1971) dimension measured on the sample.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.705570