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Optimal aggregation of classifiers in statistical learning
Open accessAbstract
Classification can be considered as nonparametric estimation of sets, where the risk is defined by means of a specific distance between sets associated with misclassification error. It is shown that the rates of convergence of classifiers depend on two parameters: the complexity of the class of candidate sets and the margin parameter. The dependence is explicitly given, indicating that optimal fast rates approaching $O(n^{-1})$ can be attained, where n is the sample size, and that the proposed classifiers have the property of robustness to the margin. The main result of the paper concerns optimal aggregation of classifiers: we suggest a classifier that automatically adapts both to the complexity and to the margin, and attains the optimal fast rates, up to a logarithmic factor.
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Cites
Breiman, L. (1996) · Machine Learning · doi:10.1007/bf00058655 · Cited by 16,325
Classification And Regression Trees
Breiman, L., Friedman, J. H., Olshen, R. A., & Stone, C. J. (2017) · doi:10.1201/9781315139470 · Cited by 11,417
A Probabilistic Theory of Pattern Recognition
Devroye, L., Györfi, L., & Lugosi, G. (1996) · Stochastic Modelling and Applied Probability · doi:10.1007/978-1-4612-0711-5 · Cited by 3,274
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Vaart, A. W. V. D., Dudoit, S., & Laan, M. J. V. D. (2006) · Statistics & Decisions · doi:10.1524/stnd.2006.24.3.351 · Cited by 156
Metadata
- Authors
- Tsybakov, A. B.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2004-02-01
- Volume
- 32
- Issue
- 1
- Pages
- 135-166
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2043919728
- Cited by
- 582
- References
- 3
- FWCI
- 25.92
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
