The DOI matches its Crossref record; 5 of the 5 references it cites were found in a registry or an index.
Structural risk minimization over data-dependent hierarchies
Abstract
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.
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Citations
Cites
Cortes, C., & Vapnik, V. (1995) · Machine Learning · doi:10.1007/bf00994018 · Cited by 59,421
The Nature of Statistical Learning Theory
Vapnik, V. N. (1995) · doi:10.1007/978-1-4757-2440-0 · Cited by 39,138
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2005) · doi:10.1002/047174882x · Cited by 13,791
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
Vapnik, V. N., & Chervonenkis, A. Y. (1971) · Theory of Probability & Its Applications · doi:10.1137/1116025 · Cited by 2,448
Mackay, D. J. C. (1995) · Network Computation in Neural Systems · doi:10.1088/0954-898x/6/3/011 · Cited by 915
Cited by
Estimating the Support of a High-Dimensional Distribution
Schölkopf, B., Platt, J. C., Shawe-Taylor, J., Smola, A. J., & Williamson, R. C. (2001) · Neural Computation · doi:10.1162/089976601750264965 · Cited by 6,168
Self-citation(1999) · doi:10.1162/089976600300015565 · Cited by 2,799
Foundations of Machine Learning
Mohri, M., Rostamizadeh, A., & Talwalkar, A. (2018) · doi:10.7551/mitpress/10290.001.0001 · Cited by 1,122
Cristianini, N., Kandola, J., Elisseeff, A., & Shawe-Taylor, J. (2006) · Studies in Fuzziness and Soft Computing · doi:10.1007/3-540-33486-6_8 · Cited by 837
Self-citationBounds on Error Expectation for Support Vector Machines
Vapnik, V., & Chapelle, O. (2000) · Neural Computation · doi:10.1162/089976600300015042 · Cited by 624
Metadata
- Authors
- Shawe-Taylor, J., Bartlett, P. L., Williamson, R. C., & Anthony, M.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1998
- Volume
- 44
- Issue
- 5
- Pages
- 1926-1940
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2106491486
- Cited by
- 527
- References
- 5
- FWCI
- 28.88
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Structural risk minimization over data-dependent hierarchies. https://app.cochat.ai/papers/10.1109/18.705570
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- Shawe-Taylor, J., Bartlett, P. L., Williamson, R. C., & Anthony, M. (1998). Structural risk minimization over data-dependent hierarchies. IEEE Transactions on Information Theory. https://doi.org/10.1109/18.705570
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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